G8_Profit and Loss_Questions ~ Bed Prasad Dhakal

Questions

Question 1

The marked price of a laptop is Rs 80000. The shopkeeper allows a \(15\%\) discount on it.
1. If marked price and discount are represented by MP and D respectively, write the formula to find the discount percentage.[1]
2. Find the discount amount given on the laptop.[1]
3. Find the profit or loss of the shopkeeper if he bought the laptop at Rs 65000.[2]
1. Formula to find discount percentage is
  Discount Percent = \( \dfrac{\text{Discount}}{\text{MP}} \times 100\% \)
  orDiscount Percent = \( \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
2. Finding the discount amount
  Marked Price (MP) = Rs. \(80,000\)
  Discount = \(15\%\) of MP
  Therefore
  Discount = \( \dfrac{15}{100} \times 80,000 = 12,000 \)
  So, the discount amount is Rs. \(12,000\).
3. Finding profit or loss
  Cost Price (CP) = Rs. \(65,000\)
  Selling Price (SP) = MP – Discount = \(80,000 - 12,000 = 68,000\)
  Since SP > CP, there is a profit.
  Profit = SP – CP = \(68,000 - 65,000 = 3,000\)
  So, the shopkeeper makes a profit of Rs. \(3,000\).
The marked price of a laptop is Rs 80000. The shopkeeper allows a \(15\%\) discount on it.
1. यदि अङ्कित मूल्य र छुटलाई क्रमशः MP र D ले जनाइन्छ भने, छुट प्रतिशत पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
2. ल्यापटपमा दिइएको छुट रकम पत्ता लगाउनुहोस् । [1]
3. यदि पसलेले उक्त ल्यापटप रु. ६५,००० मा किनेका थिए भने उनलाई भएको नाफा वा नोक्सान पत्ता लगाउनुहोस् । [2]

छुट प्रतिशत पत्ता लगाउने सूत्र निम्न अनुसार छ:
छुट प्रतिशत = \( \dfrac{\text{Discount}}{\text{MP}} \times 100\% \)
वाछुट प्रतिशत = \( \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
छुट रकम निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(80,000\)
छुट = MP को \(15\%\)
त्यसैले,
छुट रकम = \( \dfrac{15}{100} \times 80,000 = 12,000 \)
तसर्थ, छुट रकम रु. \(12,000\) हो ।
नाफा वा नोक्सान निकाल्ने तरिका:
क्रय मूल्य (CP) = रु. \(65,000\)
विक्रय मूल्य (SP) = MP – छुट = \(80,000 - 12,000 = 68,000\)
यहाँ SP > CP भएकोले, नाफा हुन्छ ।
नाफा = SP – CP = \(68,000 - 65,000 = 3,000\)
तसर्थ, पसलेलाई रु. \(3,000\) नाफा हुन्छ ।

Question 2

Sagar went to the utensil shop to buy a rice cooker. The marked price of a rice cooker is Rs 5000.

If marked price MP and discount D are represented by MP and D respectively, write the formula to find the selling price SP[1]
How much discount did Sagar get while buying a rice cooker on a discount of \(8\%\)?[1]
The shopkeeper got \(15\%\) profit after selling it at a \(8\%\) discount. What was the cost price of the rice cooker?[2]

Formula to find the selling price (SP) is
SP = MP – D
Finding the discount amount
Marked Price (MP) = Rs. \(5,000\)
Discount = \(8\%\) of MP
Therefore
Discount = \( \dfrac{8}{100} \times 5,000 = 400 \)
So, Sagar got a discount of Rs. \(400\).
Finding the cost price (CP)
Selling Price (SP) = MP – Discount = \(5,000 - 400 = 4600\)
Profit=\(15\%\)
We know
\( SP=115\% \text{ of CP} \)
or\( 4600 = \dfrac{115}{100} \times \text{CP} \)
or\( \text{CP} = \dfrac{4600 \times 100}{115} = \dfrac{460,000}{115} =4000 \)
So, the cost price of the rice cooker was approximately Rs. \(4000\).

सागर एउटा भाँडा पसलमा राइस कुकर किन्न गएछन् । उक्त राइस कुकरको अङ्कित मूल्य रु. ५,००० तोकिएको छ ।
1. यदि अङ्कित मूल्यलाई MP र छुटलाई D ले जनाइन्छ भने, विक्रय मूल्य SP पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
2. \(8\%\) छुटमा राइस कुकर किन्दा सागरले कति छुट पाए होलान् ? [1]
3. \(8\%\) छुट दिएर बेच्दा पसलेलाई \(15\%\) नाफा भयो भने उक्त राइस कुकरको क्रय मूल्य कति थियो ? [2]

विक्रय मूल्य (SP) निकाल्ने सूत्र निम्न अनुसार छ:
SP = MP – D
छुट रकम निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(5,000\)
छुट = MP को \(8\%\)
त्यसैले,
छुट रकम = \( \dfrac{8}{100} \times 5,000 = 400 \)
तसर्थ, सागरले रु. \(400\) छुट पाए ।
क्रय मूल्य (CP) निकाल्ने तरिका:
विक्रय मूल्य (SP) = MP – छुट = \(5,000 - 400 = 4600\)
नाफा = \(15\%\)
हामीलाई थाहा छ,
\( SP = CP \text{ को } 115\% \)
वा\( 4600 = \dfrac{115}{100} \times \text{CP} \)
वा\( \text{CP} = \dfrac{4600 \times 100}{115} = \dfrac{460,000}{115} = 4000 \)
तसर्थ, राइस कुकरको क्रय मूल्य रु. \(4000\) थियो ।

Question 3

Pranavi bought a mobile phone of marked price Rs 12000 at a \(20\%\) discount.

Write the formula to calculate the discount amount if the discount rate is \(D\%\) and the marked price is MP.[1]
Find the discount amount on the mobile phone.[1]
Find the selling price of the mobile phone.[1]
If the mobile phone is sold at a \(4\%\) loss, find the cost price.[1]

Formula to calculate the discount amount is
Discount Amount = \( \dfrac{D}{100} \times \text{MP} \)
Finding the discount amount
Marked Price (MP) = Rs. \(12,000\)
Discount Rate = \(20\%\)
Therefore,
Discount = \( \dfrac{20}{100} \times 12,000 = 2,400 \)
So, the discount amount is Rs. \(2,400\).
Finding the selling price (SP)
SP = MP – Discount = \(12,000 - 2,400 = 9,600\)
So, the selling price of the mobile phone is Rs. \(9,600\).
Finding the cost price (CP) when sold at a \(10\%\) loss
Selling Price (SP) = Rs. \(9,600\)
Loss = \(4\%\)
Thus,
\( SP= 96 \% \times \text{CP} \)
or\( 9600 = \dfrac{96}{100} \times \text{CP} \)
or\( \text{CP} = \dfrac{9600 \times 100}{96} =10000 \)
So, the cost price of the mobile phone was Rs. \(10,000\).

प्रणवीले अङ्कित मूल्य रु. १२,००० भएको एउटा मोबाइल फोन \(२०\%\) छुटमा किनिन् ।
1. यदि छुट दर \(D\%\) र अङ्कित मूल्य MP भए छुट रकम गणना गर्ने सूत्र लेख्नुहोस् । [1]
2. मोबाइल फोनमा दिइएको छुट रकम पत्ता लगाउनुहोस् । [1]
3. मोबाइल फोनको विक्रय मूल्य पत्ता लगाउनुहोस् । [1]
4. यदि मोबाइल फोन \(४\%\) नोक्सानमा बेचिएको भए, यसको क्रय मूल्य पत्ता लगाउनुहोस् । [1]

छुट रकम गणना गर्ने सूत्र निम्न अनुसार छ:
छुट रकम = \( \dfrac{D}{100} \times \text{MP} \)
छुट रकम निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(12,000\)
छुट दर = \(20\%\)
त्यसैले,
छुट रकम = \( \dfrac{20}{100} \times 12,000 = 2,400 \)
तसर्थ, छुट रकम रु. \(2,400\) हो ।
विक्रय मूल्य (SP) निकाल्ने तरिका:
SP = MP – छुट = \(12,000 - 2,400 = 9,600\)
तसर्थ, मोबाइल फोनको विक्रय मूल्य रु. \(9,600\) हो ।
\(४\%\) नोक्सान हुँदा क्रय मूल्य (CP) निकाल्ने तरिका:
विक्रय मूल्य (SP) = रु. \(9,600\)
नोक्सान = \(4\%\)
त्यसैले,
\( SP = CP \text{ को } 96 \% \)
वा\( 9600 = \dfrac{96}{100} \times \text{CP} \)
वा\( \text{CP} = \dfrac{9600 \times 100}{96} = 10000 \)
तसर्थ, मोबाइल फोनको क्रय मूल्य रु. \(10,000\) थियो ।

Question 4

Ashok Mahato went to a stationery shop to buy a ball. He saw two balls \(A\) and \(B\). The ratio of their marked prices is \(3:2\). The marked price of ball \(A\) is Rs 3750, and that of ball \(B\) is Rs 2500. A discount of \(5\%\) is offered.

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Write the marked prices of balls \(A\) and \(B\) in proportion.[1]
If Ashok Mahato decided to buy ball \(B\), what amount should he pay for it? Find it.[2]
If the shopkeeper wanted to earn a \(10\%\) profit by selling ball \(B\) after the discount, at what price did he buy ball \(B\)?[2]

Marked prices of balls \(A\) and \(B\) in proportion is
Marked Price of A : Marked Price of B = 3:2
or3750 : 1250 = 3:2
Amount Ashok Mahato should pay for ball \(B\):
Marked Price of ball \(B\) = Rs. \(2,500\)
Discount = \(8\%\)
Therefore
SP= 92% of MP
orSP= \(\dfrac{92}{100} \times 2500\)
orSP= 2300
So, Ashok should pay Rs. 2,300for ball B.
Cost price of ball \(B\) for a \(15\%\) profit after discount:
Selling Price (after \(8\%\) discount) = Rs. 2300
Profit =\(15\%\)
Therefore
SP = \(115\%\) of CP
or\(2300 =\dfrac{115}{100} \times \) CP
orCP=\(\dfrac{2300 \times 100}{115} = 2000 \)
So, the shopkeeper bought ball \(B\) for Rs. \(2000\).

अशोक महतो एउटा बल किन्न स्टेसनरी पसलमा गएछन् । उनले त्यहाँ \(A\) र \(B\) गरी दुईवटा बलहरू देखे । ती बलहरूको अङ्कित मूल्यको अनुपात \(3:2\) छ । बल \(A\) को अङ्कित मूल्य रु. ३७५० र बल \(B\) को अङ्कित मूल्य रु. २५०० छ । दुवैमा \(5\%\) छुटको प्रस्ताव गरिएको छ ।

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बल \(A\) र \(B\) को अङ्कित मूल्यहरूलाई समानुपातमा लेख्नुहोस् । [1]
यदि अशोक महतोले बल \(B\) किन्ने निर्णय गरे भने, उनले त्यसको लागि कति रकम तिर्नुपर्छ ? पत्ता लगाउनुहोस् । [2]
छुट पछिको मूल्यमा बल \(B\) बेचेर पसलेले \(10\%\) नाफा कमाउन चाहेको भए, उनले बल \(B\) कति मूल्यमा किनेका थिए होलान् ? [2]

बल \(A\) र \(B\) को अङ्कित मूल्यको समानुपात निम्न अनुसार छ:
बल A को अङ्कित मूल्य : बल B को अङ्कित मूल्य = 3:2
वा3750 : 2500 = 3:2
अशोक महतोले बल \(B\) को लागि तिर्नुपर्ने रकम:
बल \(B\) को अङ्कित मूल्य (MP) = रु. \(2,500\)
छुट = \(5\%\)
त्यसैले,
विक्रय मूल्य (SP) = MP को 95%
वाSP = \(\dfrac{95}{100} \times 2500\)
वाSP = 2375
तसर्थ, अशोकले बल B को लागि रु. २,३७५ तिर्नुपर्छ ।
\(10\%\) नाफा कमाउन बल \(B\) को क्रय मूल्य (CP):
विक्रय मूल्य (छुट पछिको) = रु. २,३७५
नाफा = \(10\%\)
हामीलाई थाहा छ,
विक्रय मूल्य (SP) = CP को \(110\%\)
वा\(2375 = \dfrac{110}{100} \times \) CP
वाCP = \(\dfrac{2375 \times 100}{110} \approx 2159.09 \)
तसर्थ, पसलेले बल \(B\) लगभग रु. \(2159.09\) मा किनेका थिए ।

Question 5

Ganesh buys a mobile at Rs 36000. He fixed the marked price of the mobile \(30\%\) above the cost price. If he sells the mobile at a \(25\%\) discount, then

What is the marked price of the mobile?[1]
What is the discount amount?[1]
What is the selling price of the mobile?[1]
What is his profit or loss percent from that mobile? Find it.[1]

Marked price of the mobile:
Cost Price (CP) = Rs. \(36,000\)
Marked Price (MP) is \(30\%\) above CP:
MP = \( \dfrac{130}{100} \times 36,000 = 1.3 \times 36,000 = 46,800 \)
So, the marked price is Rs. \(46,800\).
Discount amount:
Discount = \(25\%\) of MP = \( \dfrac{25}{100} \times 46,800 = 11,700 \)
So, the discount amount is Rs. \(11,700\).
Selling price of the mobile:
SP = MP – Discount = \(46,800 - 11,700 = 35,100\)
So, the selling price is Rs. \(35,100\).
Profit or loss percent:
CP = Rs. \(36,000\)
SP = Rs. \(35,100\)
Since SP < CP, there is a loss.
Loss = \(36,000 - 35,100 = 900\)
Thus
Loss Percent = \( \dfrac{900}{36,000} \times 100\% = 2.5\% \)
So, Ganesh incurred a loss of \(2.5\%\).

गणेशले एउटा मोबाइल रु. ३६,००० मा किन्छन् । उनले उक्त मोबाइलको अङ्कित मूल्य क्रय मूल्यभन्दा \(30\%\) बढी निर्धारण गरे । यदि उनले मोबाइल \(25\%\) छुटमा बेच्छन् भने:
1. मोबाइलको अङ्कित मूल्य कति हुन्छ ? [1]
2. छुट रकम कति हुन्छ ? [1]
3. मोबाइलको विक्रय मूल्य कति हुन्छ ? [1]
4. उक्त मोबाइलबाट उनलाई कति प्रतिशत नाफा वा नोक्सान हुन्छ ? पत्ता लगाउनुहोस् । [1]

मोबाइलको अङ्कित मूल्य:
क्रय मूल्य (CP) = रु. \(36,000\)
अङ्कित मूल्य (MP) क्रय मूल्यभन्दा \(30\%\) बढी छ:
MP = \( \dfrac{130}{100} \times 36,000 = 1.3 \times 36,000 = 46,800 \)
तसर्थ, अङ्कित मूल्य रु. \(46,800\) हो ।
छुट रकम:
छुट = MP को \(25\%\) = \( \dfrac{25}{100} \times 46,800 = 11,700 \)
तसर्थ, छुट रकम रु. \(11,700\) हो ।
मोबाइलको विक्रय मूल्य:
SP = MP – छुट = \(46,800 - 11,700 = 35,100\)
तसर्थ, विक्रय मूल्य रु. \(35,100\) हो ।
नाफा वा नोक्सान प्रतिशत:
CP = रु. \(36,000\)
SP = रु. \(35,100\)
यहाँ SP < CP भएकोले, नोक्सान हुन्छ ।
नोक्सान = \(36,000 - 35,100 = 900\)
यसरी,
नोक्सान प्रतिशत = \( \dfrac{900}{36,000} \times 100\% = 2.5\% \)
तसर्थ, गणेशलाई \(2.5\%\) नोक्सान भयो ।

Question 6

Ram fixed the marked price of a laptop at Rs 63000 and sold it with a \(10\%\) discount.

Write the formula to find the discount percentage.[1]
At what price did Ram sell the laptop? Find it.[2]
How much discount amount was given if Ram had fixed the price at Rs 57000 and sold it at the above selling price?[2]

Formula to find the discount percentage:
Discount Percent = \( \dfrac{\text{Discount}}{\text{Marked Price}} \times 100\% \)
orDiscount Percent = \( \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
Selling price of the laptop:
Marked Price (MP) = Rs. \(63,000\)
Discount = \(10\%\)
Thus
SP=90% of MP = \( \dfrac{90}{100} \times 63,000 = 56,700 \)
So, Ram sold the laptop at Rs. \(56,700\).
Discount amount if marked price was Rs. 57,000 but sold at the same SP Rs. 56,700:
New Marked Price = Rs. 57,000
Selling Price = Rs. 56,700
Thus
Discount = MP – SP = 57,000 - 56,700 = 300
So, the discount amount would be Rs. 300.

रामले एउटा ल्यापटपको अङ्कित मूल्य रु. ६३,००० निर्धारण गरे र यसलाई \(10\%\) छुटमा बेचे ।
1. छुट प्रतिशत पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
2. रामले उक्त ल्यापटप कति मूल्यमा बेचे ? पत्ता लगाउनुहोस् । [2]
3. यदि रामले अङ्कित मूल्य रु. ५७,००० निर्धारण गरेर माथिकै विक्रय मूल्यमा बेचेका भए, कति छुट रकम दिएका हुन्थे ? [2]

छुट प्रतिशत पत्ता लगाउने सूत्र निम्न अनुसार छ:
छुट प्रतिशत = \( \dfrac{\text{Discount}}{\text{Marked Price}} \times 100\% \)
वाछुट प्रतिशत = \( \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
ल्यापटपको विक्रय मूल्य निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(63,000\)
छुट = \(10\%\)
त्यसैले,
SP = MP को 90% = \( \dfrac{90}{100} \times 63,000 = 56,700 \)
तसर्थ, रामले ल्यापटप रु. \(56,700\) मा बेचे ।
यदि अङ्कित मूल्य रु. ५७,००० र विक्रय मूल्य रु. ५६,७०० भए छुट रकम:
नयाँ अङ्कित मूल्य = रु. 57,000
विक्रय मूल्य = रु. 56,700
यसरी,
छुट रकम = MP – SP = 57,000 - 56,700 = 300
तसर्थ, छुट रकम रु. ३०० हुने थियो ।

Question 7

The marked price of a watch is Rs 1500. The shopkeeper sold the watch after a \(10\%\) discount.

Write the formula to find the discount percentage.[1]
Find the discount amount.[1]
If the shopkeeper sold the watch to make a \(8\%\) profit, then find the cost price of the watch.[2]

Formula to find the discount percentage:
Discount Percent = \( \dfrac{\text{Discount}}{\text{Marked Price}} \times 100\% \)
orDiscount Percent = \( \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
Discount amount:
Marked Price (MP) = Rs. \(1,500\)
Discount = \(10\%\) of MP = \( \dfrac{10}{100} \times 1,500 = 150 \)
So, the discount amount is Rs. \(150\).
Cost price when sold at \(5\%\) profit:
Selling Price (SP) = MP – Discount = \(1,500 - 150 = 1,350\)
Profit = \(8\%\)
Thus
SP=108 % of CP
or\(1,350 = \dfrac{108}{100} \times \text{CP}\)
\(\text{CP} = \dfrac{1,350 \times 100}{108} = \dfrac{135,000}{108} = 1,250\)
So, the cost price of the watch was Rs. \(1,250\).

एउटा घडीको अङ्कित मूल्य रु. १,५०० छ । पसलेले १०% छुट दिएर उक्त घडी बेचेछन् ।
1. छुट प्रतिशत पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
2. छुट रकम पत्ता लगाउनुहोस् । [1]
3. यदि पसलेले उक्त घडी बेचेर ८% नाफा कमाएका भए, घडीको क्रय मूल्य पत्ता लगाउनुहोस् । [2]

छुट प्रतिशत पत्ता लगाउने सूत्र निम्न अनुसार छ:
छुट प्रतिशत = \( \dfrac{\text{Discount}}{\text{Marked Price}} \times 100\% \)
वाछुट प्रतिशत = \( \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
छुट रकम निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(1,500\)
छुट = MP को \(10\%\) = \( \dfrac{10}{100} \times 1,500 = 150 \)
तसर्थ, छुट रकम रु. \(150\) हो ।
८% नाफा हुँदाको क्रय मूल्य (CP) निकाल्ने तरिका:
विक्रय मूल्य (SP) = अङ्कित मूल्य – छुट = \(1,500 - 150 = 1,350\)
नाफा = \(8\%\)
यसरी,
विक्रय मूल्य (SP) = CP को १०८%
वा\(1,350 = \dfrac{108}{100} \times \text{CP}\)
वा\(\text{CP} = \dfrac{1,350 \times 100}{108} = \dfrac{135,000}{108} = 1,250\)
तसर्थ, घडीको क्रय मूल्य रु. \(1,250\) थियो ।

Question 8

Suman went to the furniture shop to buy a set of a table and chairs. The marked price of a set of a table and 4 chairs was Rs 12000.

If the price of a table is Rs 6000, then how much is the cost for 4 chairs?[1]
Suman gets \(5\%\) discount on the set of table and chairs. Find the price after discount.[2]
If the shopkeeper earned \(14\%\) profit even after offering \(5\%\) discount, at what price did the shopkeeper purchase the set?[2]

Cost for 4 chairs:
Marked price of the set (table + 4 chairs) = Rs. \(12,000\)
Price of the table = Rs. \(6,000\)
Therefore,
Cost of 4 chairs = \(12,000 - 6,000 = 6,000\)
So, the cost for 4 chairs is Rs. \(6,000\).
Price after \(5\%\) discount:
Marked Price (MP) = Rs. \(12,000\)
Discount = \(5\%\)
Thus
SP= 95% of MP
orSP= \( \dfrac{95}{100} \times 12,000 = 11,400\)
So, Suman pays Rs. \(11,400\) after the discount.
Cost price of the set for the shopkeeper:
Selling Price after discount = Rs. \(11,400\)
Profit \(14\%\)
Thus
SP = \(114\%\) of CP
or\(11,400 = \dfrac{114}{100} \times \text{CP}\)
or\(\text{CP} = \dfrac{11,400 \times 100}{114} = \dfrac{1,140,000}{114} =10000\)
So, the shopkeeper purchased the set for Rs. \(10000\).

सुमन एउटा फर्निचर पसलमा एउटा टेबल र कुर्सीहरूको सेट किन्न गएछन् । एउटा टेबल र ४ वटा कुर्सीहरूको सेटको अङ्कित मूल्य रु. १२,००० तोकिएको थियो ।
1. यदि एउटा टेबलको मूल्य रु. ६,००० भए, ४ वटा कुर्सीहरूको मूल्य कति पर्छ ? [1]
2. सुमनले टेबल र कुर्सीको सेटमा \(5\%\) छुट पाउँछन् । छुट पछिको मूल्य पत्ता लगाउनुहोस् । [2]
3. \(5\%\) छुट दिँदा पनि पसलेले \(14\%\) नाफा कमाएका रहेछन् भने, पसलेले उक्त सेट कति मूल्यमा किनेका थिए ? [2]

४ वटा कुर्सीहरूको मूल्य निकाल्ने तरिका:
सेटको अङ्कित मूल्य (टेबल + ४ कुर्सीहरू) = रु. \(12,000\)
टेबलको मूल्य = रु. \(6,000\)
त्यसैले,
४ वटा कुर्सीहरूको मूल्य = \(12,000 - 6,000 = 6,000\)
तसर्थ, ४ वटा कुर्सीहरूको मूल्य रु. \(6,000\) हो ।
\(5\%\) छुट पछिको मूल्य निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(12,000\)
छुट = \(5\%\)
यसरी,
विक्रय मूल्य (SP) = MP को 95%
वाSP = \( \dfrac{95}{100} \times 12,000 = 11,400\)
तसर्थ, सुमनले छुट पछि रु. \(11,400\) तिर्नुपर्छ ।
पसलेले किनेको क्रय मूल्य (CP) निकाल्ने तरिका:
छुट पछिको विक्रय मूल्य (SP) = रु. \(11,400\)
नाफा = \(14\%\)
हामीलाई थाहा छ,
विक्रय मूल्य (SP) = CP को \(114\%\)
वा\(11,400 = \dfrac{114}{100} \times \text{CP}\)
वा\(\text{CP} = \dfrac{11,400 \times 100}{114} = \dfrac{1,140,000}{114} = 10000\)
तसर्थ, पसलेले उक्त सेट रु. \(10000\) मा किनेका थिए ।

Question 9

Anisha bought a scooter for Rs 300000 and sold it to Divya after \(2\) years, deducting \(20\%\) of the price. Divya sold it to Gauri at a profit of Rs 6000.

Find the selling price of Anisha.[1]
Compare the price of Anisha and Gauri of the scooter in the ratio form.[2]

Selling price of Anisha:
Cost Price for Anisha = Rs. \(300,000\)
She sold it after deducting \(20\%\) of the price (i.e., a \(20\%\) depreciation or loss):
Thus
Selling Price = 80% of 300,000= \(\dfrac{80}{100} \times 300,000 = 240,000\)
So, Anisha sold the scooter to Divya for Rs. 240,000.
Price comparison between Anisha (original buyer) and Gauri (final buyer):
Anisha’s purchase price = Rs. \(300,000\)
Divya’s purchase price = Rs. \(240,000\)
Next
Divya sold it to Gauri at a profit of Rs. 6,000, so
Gauri’s purchase price = \(240,000 + 6,000 = 246,000\)
Now, ratio of Anisha’s price to Gauri’s price is
\(300,000 : 246,000\)
or\(50 : 41\)
So, the ratio is \(50 : 41\).

अनिशाले रु. ३,००,००० मा एउटा स्कुटर किनिन् र २ वर्षपछि उक्त मूल्यको २०% कट्टा गरी दिव्यालाई बेचिन् । दिव्याले उक्त स्कुटर रु. ६,००० नाफा खाएर गौरीलाई बेचिन् ।
1. अनिशाको विक्रय मूल्य पत्ता लगाउनुहोस् । [1]
2. स्कुटरको लागि अनिशा र गौरीले तिरेको मूल्यलाई अनुपातको रूपमा तुलना गर्नुहोस् । [2]

अनिशाको विक्रय मूल्य निकाल्ने तरिका:
अनिशाको लागि क्रय मूल्य = रु. \(300,000\)
उनले मूल्यको २०% कट्टा गरी (अर्थात् २०% मूल्यह्रास वा नोक्सानमा) बेचिन:
त्यसैले,
विक्रय मूल्य = \(300,000\) को 80% = \(\dfrac{80}{100} \times 300,000 = 240,000\)
तसर्थ, अनिशाले दिव्यालाई रु. २,४०,००० मा स्कुटर बेचिन् ।
अनिशा (सुरुको खरिदकर्ता) र गौरी (अन्तिम खरिदकर्ता) को मूल्य बीचको तुलना:
अनिशाको खरिद मूल्य = रु. \(300,000\)
दिव्याको खरिद मूल्य = रु. \(240,000\)
फेरि,
दिव्याले रु. ६,००० नाफा खाएर गौरीलाई बेचिन्, त्यसैले:
गौरीको खरिद मूल्य = \(240,000 + 6,000 = 246,000\)
अब, अनिशाको मूल्य र गौरीको मूल्यको अनुपात:
\(300,000 : 246,000\)
वा\(50 : 41\)
तसर्थ, उक्त अनुपात \(50 : 41\) हो ।

Question 10

Sundar sold a piano of marked price Rs 20000 at \(15\%\) discount.

🎹🎹♪♫~

How much is the discount amount of the article whose marked price is \(MP\) and discount percentage is \(D\%\)?[1]
Find the selling price of the piano.[1]
If the piano is sold at \(20\%\) loss, find the cost price.[2]
If piano was sold at Rs. 20,825, then what would be the profit or loss? Find in percentage.[2]

Discount amount for an article with marked price \(MP\) and discount rate \(D\%\):
Discount Amount = \( \dfrac{D}{100} \times MP \)
Selling price of the piano:
Marked Price (MP) = Rs. \(20,000\)
Discount = \(15\%\)
Thus
SP=85% of MP
orSP= \( \dfrac{85}{100} \times 20,000 = 17,000\)
So, the selling price is Rs. \(17,000\).
Cost price if sold at \(20\%\) loss.
Selling Price (SP) = Rs. \(17,000\)
Loss = \(20\%\)
Thus
SP=80% of CP
or\(17,000 = \dfrac{80}{100} \times \text{CP}\)
or\(\text{CP} = \dfrac{17,000 \times 100}{80} = \dfrac{1,700,000}{80} = 21,250\)
So, the cost price was Rs. \(21,250\).
Profit or loss percent if SP was Rs. 20,825
Cost Price = Rs. \(21,250\)
Selling Price = Rs. \(20,825\)
Since SP < CP, there is a loss.
Loss = \(21,250 - 20,825= 425\)
Now
Loss Percent = \( \dfrac{425}{21,250} \times 100\% = 2\% \)
So, Sundar would have incurred a loss of 2%.

सुन्दरले अङ्कित मूल्य रु. २०,००० भएको एउटा पियानो १५% छुटमा बेचेछन् ।
🎹🎹♪♫~
1. अङ्कित मूल्य \(MP\) र छुट प्रतिशत \(D\%\) भएको वस्तुको छुट रकम कति हुन्छ ? [1]
2. पियानोको विक्रय मूल्य पत्ता लगाउनुहोस् । [1]
3. यदि पियानो २०% नोक्सानमा बेचिएको भए, यसको क्रय मूल्य पत्ता लगाउनुहोस् । [2]
4. यदि पियानो रु. २०,८२५ मा बेचिएको भए, कति प्रतिशत नाफा वा नोक्सान हुन्थ्यो ? पत्ता लगाउनुहोस् । [2]

अङ्कित मूल्य \(MP\) र छुट दर \(D\%\) भएको वस्तुको छुट रकम निकाल्ने सूत्र निम्न अनुसार छ:
छुट रकम = \( \dfrac{D}{100} \times MP \)
पियानोको विक्रय मूल्य निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(20,000\)
छुट = \(15\%\)
यसरी,
विक्रय मूल्य (SP) = MP को 85%
वाSP = \( \dfrac{85}{100} \times 20,000 = 17,000\)
तसर्थ, विक्रय मूल्य रु. \(17,000\) हो ।
२०% नोक्सान हुँदाको क्रय मूल्य (CP) निकाल्ने तरिका:
विक्रय मूल्य (SP) = रु. \(17,000\)
नोक्सान = \(20\%\)
हामीलाई थाहा छ,
SP = CP को 80%
वा\(17,000 = \dfrac{80}{100} \times \text{CP}\)
वा\(\text{CP} = \dfrac{17,000 \times 100}{80} = \dfrac{1,700,000}{80} = 21,250\)
तसर्थ, क्रय मूल्य रु. \(21,250\) थियो ।
यदि विक्रय मूल्य रु. २०,८२५ भए नाफा वा नोक्सान प्रतिशत:
क्रय मूल्य (CP) = रु. \(21,250\)
विक्रय मूल्य (SP) = रु. \(20,825\)
यहाँ SP < CP भएकोले, नोक्सान हुन्छ ।
नोक्सान रकम = \(21,250 - 20,825 = 425\)
अब,
नोक्सान प्रतिशत = \( \dfrac{425}{21,250} \times 100\% = 2\% \)
तसर्थ, सुन्दरलाई २% नोक्सान हुन्थ्यो ।

Question 11

Prabin bought a mobile phone of labelled price Rs. 12,000 at 20% discount.

How much is the discount price of an article whose marked price is MP and the discount percentage is \(D\%\)?[1]
Find the selling price of the mobile phone.[1]
If the mobile phone is sold at 20% loss, find the cost price.[2]

Discount price (i.e., discount amount) of an article with marked price \(MP\) and discount percentage \(D\%\):
Discount Amount = \( \dfrac{D}{100} \times MP \)
Selling price of the mobile phone:
Marked Price (MP) = Rs. \(12,000\)
Discount = \(20\%\)
Thus
SP=80% of MP=\( \dfrac{80}{100} \times 12,000 = 9,600\)
So, the selling price is Rs. \(9,600\).
Cost price if the mobile phone is sold at \(20\%\) loss:
Selling Price (SP) = Rs. \(9,600\)
Loss = \(20\%\)
Thus
SP=80% of CP
\(9,600 = \dfrac{80}{100} \times \text{CP}\)
\(\text{CP} = \dfrac{9,600 \times 100}{80} = \dfrac{960,000}{80} = 12,000\)
So, the cost price was Rs. \(12,000\).

प्रविनले अङ्कित मूल्य रु. १२,००० भएको एउटा मोबाइल फोन २०% छुटमा किनेछन् ।
1. अङ्कित मूल्य MP र छुट प्रतिशत \(D\%\) भएको वस्तुको छुट रकम कति हुन्छ ? [1]
2. मोबाइल फोनको विक्रय मूल्य पत्ता लगाउनुहोस् । [1]
3. यदि मोबाइल फोन २०% नोक्सानमा बेचिएको भए, यसको क्रय मूल्य पत्ता लगाउनुहोस् । [2]

अङ्कित मूल्य \(MP\) र छुट प्रतिशत \(D\%\) भएको वस्तुको छुट रकम निकाल्ने सूत्र निम्न अनुसार छ:
छुट रकम = \( \dfrac{D}{100} \times MP \)
मोबाइल फोनको विक्रय मूल्य निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(12,000\)
छुट = \(20\%\)
यसरी,
विक्रय मूल्य (SP) = MP को 80% = \( \dfrac{80}{100} \times 12,000 = 9,600\)
तसर्थ, मोबाइल फोनको विक्रय मूल्य रु. \(9,600\) हो ।
२०% नोक्सान हुँदाको क्रय मूल्य (CP) निकाल्ने तरिका:
विक्रय मूल्य (SP) = रु. \(9,600\)
नोक्सान = \(20\%\)
हामीलाई थाहा छ,
विक्रय मूल्य (SP) = CP को 80%
वा \(9,600 = \dfrac{80}{100} \times \text{CP}\)
वा \(\text{CP} = \dfrac{9,600 \times 100}{80} = \dfrac{960,000}{80} = 12,000\)
तसर्थ, मोबाइल फोनको क्रय मूल्य रु. \(12,000\) थियो ।

Question 12

Anish marked the price of a radio Rs. 3000. If he sold it allowing a discount of \(15\%\) and made a profit of Rs. 500.

If marked price (MP) and discount percent (D) are represented by (MP) and (D) respectively, write the formula to find the selling price.[1]
What is the selling price of the radio?[1]
If the discount was not allowed, then what would be the profit?[2]

Formula to find the selling price (SP) using marked price (MP) and discount percent (D):
SP = MP – D% of MP
Selling price of the radio:
Marked Price (MP) = Rs. \(3,000\)
Discount = \(15\%\)
Thus
SP = 85%of MP = \( \dfrac{85}{100} \times 3,000 = 2,550\)
So, the selling price is Rs. 2,550.
Profit if no discount was allowed.
From part (ii), we got SP = Rs. 2,550, and Profit = Rs. 500
Thus
Cost Price (CP) = SP – Profit = 2,550 - 500 = 2,050
Now
CP=2050
SP=3,000
Then
Profit= SP – CP = 3000-2050=950
So, the new profit would be Rs. 950.

अनिशले एउटा रेडियोको अङ्कित मूल्य रु. ३,००० निर्धारण गरे । यदि उनले १५% छुट दिएर रेडियो बेच्दा रु. ५०० नाफा कमाए भने:
1. यदि अङ्कित मूल्य (MP) र छुट प्रतिशत (D) लाई क्रमशः (MP) र (D) ले जनाइन्छ भने, विक्रय मूल्य पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
2. रेडियोको विक्रय मूल्य कति हुन्छ ? [1]
3. यदि छुट नदिइएको भए, नाफा कति हुन्थ्यो ? [2]

अङ्कित मूल्य (MP) र छुट प्रतिशत (D) प्रयोग गरेर विक्रय मूल्य (SP) निकाल्ने सूत्र निम्न अनुसार छ:
SP = MP – MP को D%
रेडियोको विक्रय मूल्य निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(3,000\)
छुट = \(15\%\)
यसरी,
विक्रय मूल्य (SP) = MP को 85% = \( \dfrac{85}{100} \times 3,000 = 2,550\)
तसर्थ, विक्रय मूल्य रु. २,५५० हो ।
यदि छुट नदिइएको भए हुने नाफा निकाल्ने तरिका:
भाग (ii) बाट, हामीले SP = रु. २,५५० र नाफा = रु. ५०० पायौँ ।
यसरी,
क्रय मूल्य (CP) = SP – नाफा = 2,550 - 500 = 2,050
अब,
यदि छुट नदिने हो भने नयाँ विक्रय मूल्य (SP) = अङ्कित मूल्य = रु. ३,००० हुन्छ ।
क्रय मूल्य (CP) = रु. २,०५०
त्यसैले,
नयाँ नाफा = SP – CP = 3,000 - 2,050 = 950
तसर्थ, नयाँ नाफा रु. ९५० हुने थियो ।

Question 13

Ramdev went to utensil shop to buy a rice cooker. The marked price of a rice cooker is Rs. 6000.

If marked price and discount are represented by (MP) and (D) respectively, write the formula to find the selling price.[1]
How much discount did Ramdev get while buying a rice cooker on discount of 15%?[1]
The shopkeeper got 20% profit after selling it at 15% discount. What was the cost price of the rice cooker?[2]

Formula to find the selling price (SP) using marked price (MP) and discount (D):
SP = MP – D
or, if discount is given as a percentage \(D\%\):
SP = \( (100-D)\% \times MP \)
Discount amount received by Ramdev.
Marked Price (MP) = Rs. 6,000
Discount = \(15\%\)
Thus
Discount = \(15\% \times MP= \dfrac{15}{100} \times 6,000 = 900 \)
So, Ramdev got a discount of Rs. \(900\).
Cost price of the rice cooker
We know that
Selling Price (SP) = MP – Discount = \(6,000 - 900 = 5,100\)
Given that
Profit = \(20\%\)
Thus
SP= 120% of CP
or\(5100= \dfrac{120}{100} \times\) CP
or \(\text{CP} = \dfrac{5100 \times 100}{120} = 4250\)
So, the cost price of the rice cooker was Rs. 4250.

रामदेव एउटा भाँडा पसलमा राइस कुकर किन्न गएछन् । उक्त राइस कुकरको अङ्कित मूल्य रु. ६,००० तोकिएको छ ।
1. यदि अङ्कित मूल्य र छुटलाई क्रमशः (MP) र (D) ले जनाइन्छ भने, विक्रय मूल्य पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
2. १५% छुटमा राइस कुकर किन्दा रामदेवले कति छुट पाए होलान् ? [1]
3. १५% छुट दिएर बेच्दा पसलेलाई 20 % नाफा भयो भने उक्त राइस कुकरको क्रय मूल्य कति थियो ? [2]

अङ्कित मूल्य (MP) र छुट (D) प्रयोग गरेर विक्रय मूल्य (SP) निकाल्ने सूत्र निम्न अनुसार छ:
SP = MP – D
वा, यदि छुट प्रतिशत \(D\%\) मा दिइएको छ भने:
SP = \( (100-D)\% \times MP \)
रामदेवले पाएको छुट रकम
अङ्कित मूल्य (MP) = रु. ६,०००
छुट = \(15\%\)
यसरी,
छुट रकम = \(MP \text{ को } 15\% = \dfrac{15}{100} \times 6,000 = 900 \)
तसर्थ, रामदेवले रु. \(900\) छुट पाए ।
राइस कुकरको क्रय मूल्य
हामीलाई थाहा छ,
विक्रय मूल्य (SP) = MP – छुट रकम = \(6,000 - 900 = 5,100\)
दिइएको छ,
नाफा = \(20\%\)
यसरी,
SP = CP \text{ को } 115%
वा \(5100 = \dfrac{120}{100} \times \text{CP}\)
वा \(\text{CP} = \dfrac{5100 \times 100}{120} \approx 42250\)
तसर्थ, राइस कुकरको क्रय मूल्य 42250 थियो ।

Question 14

Anup bought a mobile phone labelled at Rs. 12,000 at a 20% discount.

How much is the discount price of an article whose marked price is (M.P.) and discount percentage is (D%)?[1]
Find the selling price of the mobile phone.[1]
If the mobile phone is sold at a 20% loss, find the cost price.[2]

Discount amount of an article with marked price (M.P.) and discount percentage (D%):
Discount Amount = \( \dfrac{D}{100} \times \text{M.P.} \)
Selling price of the mobile phone.
Marked Price (M.P.) = Rs. \(12,000\)
Discount = \(20\%\)
Thus
SP=80% of MP = \( \dfrac{80}{100} \times 12,000 = 9,600\)
So, the selling price is Rs. \(9,600\).
Cost price if the mobile phone is sold at a \(20\%\) loss.
Selling Price (SP) = Rs. \(9,600\)
Loss=20%
Thus
SP=\(80\%\) of Cost Price (CP).
or\(9,600 = \dfrac{80}{100} \times \text{CP}\)
or\(\text{CP} = \dfrac{9,600 \times 100}{80} = \dfrac{960,000}{80} = 12,000\)
So, the cost price was Rs. \(12,000\).

अनूपले अङ्कित मूल्य रु. १२,००० भएको एउटा मोबाइल फोन २०% छुटमा किनेछन् ।
1. अङ्कित मूल्य (M.P.) र छुट प्रतिशत (D%) भएको वस्तुको छुट रकम कति हुन्छ ? [1]
2. मोबाइल फोनको विक्रय मूल्य पत्ता लगाउनुहोस् । [1]
3. यदि मोबाइल फोन २०% नोक्सानमा बेचिएको भए, यसको क्रय मूल्य पत्ता लगाउनुहोस् । [2]

अङ्कित मूल्य (M.P.) र छुट प्रतिशत (D%) भएको वस्तुको छुट रकम:
छुट रकम = \( \dfrac{D}{100} \times \text{M.P.} \)
मोबाइल फोनको विक्रय मूल्य:
अङ्कित मूल्य (M.P.) = रु. \(12,000\)
छुट = \(20\%\)
यसरी,
SP = MP को 80% = \( \dfrac{80}{100} \times 12,000 = 9,600\)
तसर्थ, विक्रय मूल्य रु. \(9,600\) हो ।
२०% नोक्सानमा मोबाइल फोन बेच्दाको क्रय मूल्य:
विक्रय मूल्य (SP) = रु. \(9,600\)
नोक्सान = 20%
यसरी,
SP = क्रय मूल्य (CP) को \(80\%\)
वा \(9,600 = \dfrac{80}{100} \times \text{CP}\)
वा \(\text{CP} = \dfrac{9,600 \times 100}{80} = \dfrac{960,000}{80} = 12,000\)
तसर्थ, क्रय मूल्य रु. \(12,000\) थियो ।

Question 15

A shopkeeper marked the price Rs 60000 for a computer and sold it with \(10\%\) discount.

If marked price and discount percent are denoted by \(MP\) and \(D\%\) respectively, write the formula to find the discount amount.[1]
What will be the discount amount if \(10\%\) discount is given?[1]
Selling after \(10\%\) discount, it becomes a profit of Rs 4000. Find the cost price.[2]

Formula to find the discount amount:
Discount Amount = \( \dfrac{D}{100} \times MP \)
Discount amount
Marked Price (MP) = Rs. 60,000
Discount = \(10\%\)
Thus
Discount Amount = \( \dfrac{10}{100} \times 60,000 = 6,000 \)
So, the discount amount is Rs. \(6,000\).
Cost price
Marked Price (MP) = Rs. 60,000
Discount = \(10\%\)
Thus
Selling Price (SP) = 90% of MP = \( \dfrac{90}{100} \times 60,000 = 54,000 \)
Profit = Rs. 4,000
We know
CP =SP-profit= \(54,000 - 4,000 = 50,000\)
So, the cost price was Rs. 50,000.

एकजना पसलेले एउटा कम्प्युटरको अङ्कित मूल्य रु. ६०,००० निर्धारण गरे र १०% छुट दिएर बेचे ।
1. यदि अङ्कित मूल्य र छुट प्रतिशतलाई क्रमशः \(MP\) र \(D\%\) ले जनाइन्छ भने, छुट रकम पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
2. यदि १०% छुट दिइन्छ भने छुट रकम कति हुन्छ ? [1]
3. १०% छुट दिएर बेच्दा रु. ४,००० नाफा हुन्छ भने उक्त कम्प्युटरको क्रय मूल्य पत्ता लगाउनुहोस् । [2]

छुट रकम पत्ता लगाउने सूत्र:
छुट रकम = \( \dfrac{D}{100} \times MP \)
छुट रकम:
अङ्कित मूल्य (MP) = रु. ६०,०००
छुट = \(10\%\)
यसरी,
छुट रकम = \( \dfrac{10}{100} \times 60,000 = 6,000 \)
तसर्थ, छुट रकम रु. \(6,000\) हो ।
क्रय मूल्य:
अङ्कित मूल्य (MP) = रु. ६०,०००
छुट = \(10\%\)
यसरी,
विक्रय मूल्य (SP) = MP को 90% = \( \dfrac{90}{100} \times 60,000 = 54,000 \)
नाफा = रु. ४,०००
हामीलाई थाहा छ,
CP = SP - नाफा = \(54,000 - 4,000 = 50,000\)
तसर्थ, क्रय मूल्य रु. ५०,००० थियो ।

Question 16

The cost of a mobile is Rs 12800. However, the mobile's marked price is \(20\%\) above the cost price. The shopkeeper sold the mobile, allowing a \(10\%\) discount.

Find the marked price of the mobile.[2]
Find the selling price of the mobile.[2]
What is the shopkeeper's profit or loss percent from the mobile? Find it.[1]

Marked price of the mobile.
Cost Price (CP) = Rs. \(12,800\)
Marked Price is \(20\%\) above CP.
Thus
MP = 120% of CP = \( \dfrac{120}{100} \times 12,800 = 15,360 \)
So, the marked price is Rs. \(15,360\).
Selling price of the mobile.
Marked Price (MP) = Rs. \(15,360\)
Discount = \(10\%\)
Thus
SP = 90% of MP = \( \dfrac{90}{100} \times 15,360 = 13,824 \)
So, the selling price is Rs. \(13,824\).
Profit or loss percent.
Cost Price (CP) = Rs. \(12,800\)
Selling Price (SP) = Rs. \(13,824\)
Since SP > CP, there is a profit.
Profit = \(13,824 - 12,800 = 1,024\)
Thus
Profit Percent = \( \dfrac{1,024}{12,800} \times 100\% = 8\% \)
So, the shopkeeper made a profit of \(8\%\).

एउटा मोबाइलको क्रय मूल्य रु. १२,८०० छ । उक्त मोबाइलको अङ्कित मूल्य क्रय मूल्यभन्दा २०% बढी निर्धारण गरिएको छ । पसलेले १०% छुट दिएर मोबाइल बेचेछन् भने:
1. मोबाइलको अङ्कित मूल्य पत्ता लगाउनुहोस् । [2]
2. मोबाइलको विक्रय मूल्य पत्ता लगाउनुहोस् । [2]
3. उक्त मोबाइलबाट पसलेलाई कति प्रतिशत नाफा वा नोक्सान भयो ? पत्ता लगाउनुहोस् । [1]

मोबाइलको अङ्कित मूल्य:
क्रय मूल्य (CP) = रु. \(12,800\)
अङ्कित मूल्य (MP) क्रय मूल्यभन्दा २०% बढी छ ।
यसरी,
MP = CP को 120% = \( \dfrac{120}{100} \times 12,800 = 15,360 \)
तसर्थ, अङ्कित मूल्य रु. \(15,360\) हो ।
मोबाइलको विक्रय मूल्य:
अङ्कित मूल्य (MP) = रु. \(15,360\)
छुट = १०%
यसरी,
SP = MP को 90% = \( \dfrac{90}{100} \times 15,360 = 13,824 \)
तसर्थ, विक्रय मूल्य रु. \(13,824\) हो ।
नाफा वा नोक्सान प्रतिशत:
क्रय मूल्य (CP) = रु. \(12,800\)
विक्रय मूल्य (SP) = रु. \(13,824\)
यहाँ SP > CP भएकोले, नाफा हुन्छ ।
नाफा रकम = \(13,824 - 12,800 = 1,024\)
यसरी,
नाफा प्रतिशत = \( \dfrac{1,024}{12,800} \times 100\% = 8\% \)
तसर्थ, पसलेलाई ८% नाफा भयो ।

Question 17

A mobile set of marked price Rs 22000 is sold at \(10\%\) discount.

Write the formula to find the discount amount.[1]
Find the discount amount of the mobile set.[1]
Find the selling price of the mobile.[1]

Formula to find the discount amount:
Discount Amount = \( \dfrac{D}{100} \times \text{MP} \)
Discount amount of the mobile set.
Marked Price (MP) = Rs. \(22,000\)
Discount = \(10\%\)
Thus
Discount Amount = \( \dfrac{10}{100} \times 22,000 = 2,200 \)
So, the discount amount is Rs. \(2,200\).
Selling price of the mobile.
Marked Price (MP) = Rs. \(22,000\)
Discount = \(10\%\)
Thus
SP = 90% of MP = \( \dfrac{90}{100} \times 22,000 = 19,800 \)
So, the selling price is Rs. \(19,800\).

अङ्कित मूल्य रु. २२,००० भएको एउटा मोबाइल सेट १०% छुटमा बेचियो ।
1. छुट रकम पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
2. मोबाइल सेटको छुट रकम पत्ता लगाउनुहोस् । [1]
3. मोबाइलको विक्रय मूल्य पत्ता लगाउनुहोस् । [1]

छुट रकम पत्ता लगाउने सूत्र:
छुट रकम = \( \dfrac{D}{100} \times \text{MP} \)
मोबाइल सेटको छुट रकम:
अङ्कित मूल्य (MP) = रु. \(22,000\)
छुट = १०%
यसरी,
छुट रकम = \( \dfrac{10}{100} \times 22,000 = 2,200 \)
तसर्थ, छुट रकम रु. २,२०० हो ।
मोबाइलको विक्रय मूल्य:
अङ्कित मूल्य (MP) = रु. \(22,000\)
छुट = १०%
यसरी,
SP = MP को 90% = \( \dfrac{90}{100} \times 22,000 = 19,800 \)
तसर्थ, विक्रय मूल्य रु. १९,८०० हो ।

Question 18

The marked price of a bag is Rs 5000.

If marked price and discount percent are represented by \(MP\) and \(D\%\) respectively, write the formula to find the discount percent.[1]
How much will be the discount amount of the bag if a discount of \(5\%\) on the marked price is given?[1]
The shopkeeper gets \(25\%\) profit after selling the bag at \(5\%\) discount. What was the cost price of the bag?[2]

Formula to find the discount percent:
Discount Percent = \( \dfrac{\text{Discount Amount}}{MP} \times 100\% \)
orDiscount Percent = \( \dfrac{MP - SP}{MP} \times 100\% \)
Discount amount
Marked Price (MP) = Rs. \(5,000\)
Discount = \(5\%\)
Thus
Discount Amount = \( \dfrac{5}{100} \times 5,000 = 250 \)
So, the discount amount is Rs. \(250\).
Cost price
Marked Price (MP) = Rs. \(5,000\)
Discount = \(5\%\)
Thus
Selling Price (SP) = 95% of MP = \( \dfrac{95}{100} \times 5,000 = 4,750 \)
Profit = \(25\%\)
Thus
SP= 125% of CP
\(4,750 = \dfrac{125}{100} \times \text{CP}\)
or\(\text{CP} = \dfrac{4,750 \times 100}{125} = \dfrac{475,000}{125} = 3,800\)
So, the cost price of the bag was Rs. \(3,800\).

एउटा झोलाको अङ्कित मूल्य रु. ५,००० छ ।
1. यदि अङ्कित मूल्य र छुट प्रतिशतलाई क्रमशः \(MP\) र \(D\%\) ले जनाइन्छ भने, छुट प्रतिशत पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
2. यदि अङ्कित मूल्यमा ५% छुट दिइन्छ भने झोलाको छुट रकम कति हुन्छ ? [1]
3. ५% छुट दिएर झोला बेच्दा पसलेलाई २५% नाफा हुन्छ भने उक्त झोलाको क्रय मूल्य कति थियो ? [2]

छुट प्रतिशत पत्ता लगाउने सूत्र:
छुट प्रतिशत = \( \dfrac{\text{Discount Amount}}{MP} \times 100\% \)
वा छुट प्रतिशत = \( \dfrac{MP - SP}{MP} \times 100\% \)
छुट रकम:
अङ्कित मूल्य (MP) = रु. \(5,000\)
छुट = ५%
यसरी,
छुट रकम = \( \dfrac{5}{100} \times 5,000 = 250 \)
तसर्थ, छुट रकम रु. २५० हो ।
क्रय मूल्य:
अङ्कित मूल्य (MP) = रु. \(5,000\)
छुट = ५%
यसरी,
विक्रय मूल्य (SP) = MP को 95% = \( \dfrac{95}{100} \times 5,000 = 4,750 \)
नाफा = २५%
हामीलाई थाहा छ,
SP = CP को 125%
वा \(4,750 = \dfrac{125}{100} \times \text{CP}\)
वा \(\text{CP} = \dfrac{4,750 \times 100}{125} = \dfrac{475,000}{125} = 3,800\)
तसर्थ, झोलाको क्रय मूल्य रु. ३,८०० थियो ।

Question 19

Ramu marked the price of a mobile at Rs 80000. He sold it with a \(10\%\) discount and gained a profit of Rs 4000.

Write the formula for profit.[1]
Find the discount amount.[1]
Find the cost price of the mobile.[1]

Formula for profit:
Profit = Selling Price (SP) – Cost Price (CP)
Discount amount.
Marked Price (MP) = Rs. \(80,000\)
Discount = \(10\%\)
Thus
Discount Amount = \( \dfrac{10}{100} \times 80,000 = 8,000 \)
So, the discount amount is Rs. \(8,000\).
Cost price of the mobile.
Marked Price (MP) = Rs. \(80,000\)
Discount = \(10\%\)
Thus
Selling Price (SP) = 90% of MP = \( \dfrac{90}{100} \times 80,000 = 72,000 \)
Profit = Rs. \(4,000\)
We know that
CP = SP – Profit
orCP = \(72,000 - 4,000 = 68,000\)
So, the cost price of the mobile was Rs. \(68,000\).

रामुले एउटा मोबाइलको अङ्कित मूल्य रु. ८०,००० निर्धारण गरे । उनले उक्त मोबाइल १०% छुटमा बेच्दा रु. ४,००० नाफा कमाए भने:
1. नाफा पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
2. छुट रकम पत्ता लगाउनुहोस् । [1]
3. मोबाइलको क्रय मूल्य पत्ता लगाउनुहोस् । [1]

नाफा पत्ता लगाउने सूत्र:
नाफा = विक्रय मूल्य (SP) – क्रय मूल्य (CP)
छुट रकम:
अङ्कित मूल्य (MP) = रु. \(80,000\)
छुट = १०%
यसरी,
छुट रकम = \( \dfrac{10}{100} \times 80,000 = 8,000 \)
तसर्थ, छुट रकम रु. ८,००० हो ।
मोबाइलको क्रय मूल्य:
अङ्कित मूल्य (MP) = रु. \(80,000\)
छुट = १०%
यसरी,
विक्रय मूल्य (SP) = MP को 90% = \( \dfrac{90}{100} \times 80,000 = 72,000 \)
नाफा = रु. \(4,000\)
हामीलाई थाहा छ,
क्रय मूल्य (CP) = SP – नाफा
वा CP = \(72,000 - 4,000 = 68,000\)
तसर्थ, मोबाइलको क्रय मूल्य रु. ६८,००० थियो ।

Question 20

Kreepa marks a laptop with a price of Rs 120000.

If profit percent, cost price, and selling price are denoted by \(P\%\), \(C.P.\), and \(S.P.\) respectively, write the formula to find cost price (\(C.P.\)).[1]
What will be the price of the laptop if a \(15\%\) discount is given?[2]
Find the cost price if the profit amount is Rs 10000.[1]

Formula to find cost price
\( SP =(100 + P)\% \times CP \)
or equivalently,
\( CP= \dfrac{100}{100 + P} \times SP \)
Price of the laptop after a \(15\%\) discount.
Marked Price (MP) = Rs. \(120,000\)
Discount = \(15\%\)
Thus
Selling Price = 85% of MP = \( \dfrac{85}{100} \times 120,000 = 102,000 \)
So, the price after discount is Rs. \(102,000\).
Cost price
From part (ii), we get that
Selling Price (SP) = Rs. \(102,000\)
Profit = Rs. \(10,000\)
We know that
CP = SP-profit=\(102,000 - 10,000 = 92,000\)
So, the cost price was Rs. \(92,000\).

कृपाले एउटा ल्यापटपको अङ्कित मूल्य रु. १,२०,००० निर्धारण गरिन् ।
1. यदि नाफा प्रतिशत, क्रय मूल्य र विक्रय मूल्यलाई क्रमशः \(P\%\), \(C.P.\), र \(S.P.\) ले जनाइन्छ भने, क्रय मूल्य (\(C.P.\)) पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
2. यदि १५% छुट दिइन्छ भने उक्त ल्यापटपको मूल्य कति हुन्छ ? [2]
3. यदि नाफा रकम रु. १०,००० भए, क्रय मूल्य पत्ता लगाउनुहोस् । [1]

क्रय मूल्य पत्ता लगाउने सूत्र:
\( SP = (100 + P)\% \times CP \)
वा,
\( CP = \dfrac{100}{100 + P} \times SP \)
१५% छुट पछिको ल्यापटपको मूल्य:
अङ्कित मूल्य (MP) = रु. \(120,000\)
छुट = १५%
यसरी,
विक्रय मूल्य (SP) = MP को 85% = \( \dfrac{85}{100} \times 120,000 = 102,000 \)
तसर्थ, छुट पछिको मूल्य रु. \(102,000\) हो ।
क्रय मूल्य:
भाग (ii) बाट, हामीले प्राप्त गर्यौँ:
विक्रय मूल्य (SP) = रु. \(102,000\)
नाफा = रु. \(10,000\)
हामीलाई थाहा छ,
CP = SP - नाफा = \(102,000 - 10,000 = 92,000\)
तसर्थ, क्रय मूल्य रु. ९२,००० थियो ।

Question 21

The marked price of a watch is Rs 1500. A shopkeeper sold it at \(10\%\) discount.

Write the formula to calculate discount percentage.[1]
Find the discount amount.[1]
If the shopkeeper earns a profit of \(8\%\) by selling the watch, at what price did he buy the watch?[2]

Formula to calculate discount percentage:
Discount Percent = \( \dfrac{\text{Discount Amount}}{\text{Marked Price}} \times 100\% \)
orDiscount Percent = \( \dfrac{MP - SP}{MP} \times 100\% \)
Discount amount.
Marked Price (MP) = Rs. \(1,500\)
Discount = \(10\%\)
Thus
Discount Amount = \( \dfrac{10}{100} \times 1,500 = 150 \)
So, the discount amount is Rs. \(150\).
Cost price when the shopkeeper earns an \(8\%\) profit.
Marked Price (MP) = Rs. \(1,500\)
Discount = \(10\%\)
Thus
Selling Price (SP) = 90% of MP = \( \dfrac{90}{100} \times 1,500 = 1,350 \)
Now, given that
Profit = \(8\%\)
Therefore
, so SP = \(108\%\) of CP.
Thus
SP = 108% of CP
or\(1,350 = \dfrac{108}{100} \times \text{CP}\)
or\(\text{CP} = \dfrac{1,350 \times 100}{108} = \dfrac{135,000}{108} = 1,250\)
So, the shopkeeper bought the watch for Rs. \(1,250\).

एउटा घडीको अङ्कित मूल्य रु. १,५०० छ । पसलेले १०% छुट दिएर उक्त घडी बेचेछन् ।
1. छुट प्रतिशत गणना गर्ने सूत्र लेख्नुहोस् । [1]
2. छुट रकम पत्ता लगाउनुहोस् । [1]
3. यदि पसलेले उक्त घडी बेचेर ८% नाफा कमाएका भए, उनले उक्त घडी कतिमा किनेका थिए ? [2]

छुट प्रतिशत गणना गर्ने सूत्र:
छुट प्रतिशत = \( \dfrac{\text{Discount Amount}}{\text{Marked Price}} \times 100\% \)
वा छुट प्रतिशत = \( \dfrac{MP - SP}{MP} \times 100\% \)
छुट रकम:
अङ्कित मूल्य (MP) = रु. \(1,500\)
छुट = १०%
यसरी,
छुट रकम = \( \dfrac{10}{100} \times 1,500 = 150 \)
तसर्थ, छुट रकम रु. १५० हो ।
८% नाफा हुँदाको क्रय मूल्य:
अङ्कित मूल्य (MP) = रु. \(1,500\)
छुट = १०%
यसरी,
विक्रय मूल्य (SP) = MP को 90% = \( \dfrac{90}{100} \times 1,500 = 1,350 \)
दिइएको छ,
नाफा = ८%
यसर्थ, SP = CP को १०८% हुन्छ ।
हामीलाई थाहा छ,
SP = CP को 108%
वा \(1,350 = \dfrac{108}{100} \times \text{CP}\)
वा \(\text{CP} = \dfrac{1,350 \times 100}{108} = \dfrac{135,000}{108} = 1,250\)
तसर्थ, पसलेले उक्त घडी रु. १,२५० मा किनेका थिए ।

Question 22

The marked price of a book is Rs 3900.

If marked price and discount are represented by \(M\) and \(D\) respectively, write the formula to find the discount percent.[1]
If the discount percent is \(7\%\), how much discount is given?[1]
If the shopkeeper earned a \(17\%\) profit after selling it at \(7\%\) discount, find the cost price of the book.[2]

Formula to find the discount percent:
Discount Percent = \( \dfrac{D}{M} \times 100\% \)
orDiscount Percent = \( \dfrac{M - SP}{M} \times 100\% \)
Discount amount
Marked Price (\(M\)) = Rs. \(3,900\)
Discount Percent = \(7\%\)
Thus
Discount = \( \dfrac{7}{100} \times 3,900 = 273 \)
So, the discount given is Rs. \(273\).
Cost price
Marked Price (\(M\)) = Rs. \(3,900\)
Discount = \(7\%\)
Thus
Selling Price (SP) = 93% of MP = \( \dfrac{93}{100} \times 3,900 = 3,627 \)
Given that
Profit = \(17\%\)
Thus
SP = 117% of CP
or\(3,627 = \dfrac{117}{100} \times \text{CP}\)
or\(\text{CP} = \dfrac{3,627 \times 100}{117} = \dfrac{362,700}{117} = 3,100\)
So, the cost price of the book was Rs. \(3,100\).

एउटा किताबको अङ्कित मूल्य रु. ३,९०० छ ।
1. यदि अङ्कित मूल्य र छुटलाई क्रमशः \(M\) र \(D\) ले जनाइन्छ भने, छुट प्रतिशत पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
2. यदि छुट प्रतिशत ७% भए, छुट रकम कति हुन्छ ? [1]
3. ७% छुट दिएर किताब बेच्दा पसलेले १७% नाफा कमाएका रहेछन् भने, उक्त किताबको क्रय मूल्य पत्ता लगाउनुहोस् । [2]

छुट प्रतिशत पत्ता लगाउने सूत्र:
छुट प्रतिशत = \( \dfrac{D}{M} \times 100\% \)
वा छुट प्रतिशत = \( \dfrac{M - SP}{M} \times 100\% \)
छुट रकम:
अङ्कित मूल्य (\(M\)) = रु. \(3,900\)
छुट प्रतिशत = ७%
यसरी,
छुट रकम = \( \dfrac{7}{100} \times 3,900 = 273 \)
तसर्थ, दिइएको छुट रु. २७३ हो ।
क्रय मूल्य:
अङ्कित मूल्य (\(M\)) = रु. \(3,900\)
छुट = ७%
यसरी,
विक्रय मूल्य (SP) = MP को 93% = \( \dfrac{93}{100} \times 3,900 = 3,627 \)
दिइएको छ,
नाफा = १७%
हामीलाई थाहा छ,
SP = CP को 117%
वा \(3,627 = \dfrac{117}{100} \times \text{CP}\)
वा \(\text{CP} = \dfrac{3,627 \times 100}{117} = \dfrac{362,700}{117} = 3,100\)
तसर्थ, किताबको क्रय मूल्य रु. ३,१०० थियो ।

Question 23

Ganesh bought a laptop for Rs 75000 and fixed its marked price \(20\%\) above the cost price. The laptop is sold to Ramesh after allowing a \(20\%\) discount.

Write the formula to find the discount percentage.[1]
Find the marked price of the laptop.[1]
What is Ganesh’s profit or loss percent in this transaction? Calculate it.[2]

Formula to find the discount percentage:
Discount Percent = \( \dfrac{\text{Discount Amount}}{\text{Marked Price}} \times 100\% \)
orDiscount Percent = \( \dfrac{MP - SP}{MP} \times 100\% \)
Marked price of the laptop.
Cost Price (CP) = Rs. \(75,000\)
Marked Price is \(20\%\) above CP.
Thus
MP = 120% of CP = \( \dfrac{120}{100} \times 75,000 = 90,000 \)
So, the marked price is Rs. \(90,000\).
Profit or loss percent in the transaction.
Marked Price (MP) = Rs. \(90,000\)
Discount = \(20\%\)
Thus
Selling Price (SP) = 80% of MP = \( \dfrac{80}{100} \times 90,000 = 72,000 \)
Given that
Cost Price (CP) = Rs. \(75,000\)
Since SP < CP, there is a loss. So
Loss = \(75,000 - 72,000 = 3,000\)
Now
Loss Percent = \( \dfrac{3,000}{75,000} \times 100\% = 4\% \)
So, Ganesh incurred a loss of \(4\%\).

गणेशले एउटा ल्यापटप रु. ७५,००० मा किने र यसको अङ्कित मूल्य क्रय मूल्यभन्दा २०% बढी निर्धारण गरे । उनले २०% छुट दिएर उक्त ल्यापटप रमेशलाई बेचे भने:
1. छुट प्रतिशत पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
2. ल्यापटपको अङ्कित मूल्य पत्ता लगाउनुहोस् । [1]
3. यस कारोबारमा गणेशलाई कति प्रतिशत नाफा वा नोक्सान भयो ? गणना गर्नुहोस् । [2]

छुट प्रतिशत पत्ता लगाउने सूत्र:
छुट प्रतिशत = \( \dfrac{\text{Discount Amount}}{\text{Marked Price}} \times 100\% \)
वा छुट प्रतिशत = \( \dfrac{MP - SP}{MP} \times 100\% \)
ल्यापटपको अङ्कित मूल्य:
क्रय मूल्य (CP) = रु. \(75,000\)
अङ्कित मूल्य क्रय मूल्यभन्दा २०% बढी छ ।
यसरी,
MP = CP को 120% = \( \dfrac{120}{100} \times 75,000 = 90,000 \)
तसर्थ, अङ्कित मूल्य रु. ९०,००० हो ।
कारोबारमा भएको नाफा वा नोक्सान प्रतिशत:
अङ्कित मूल्य (MP) = रु. \(90,000\)
छुट = २०%
यसरी,
विक्रय मूल्य (SP) = MP को 80% = \( \dfrac{80}{100} \times 90,000 = 72,000 \)
दिइएको छ,
क्रय मूल्य (CP) = रु. \(75,000\)
यहाँ SP < CP भएकोले, नोक्सान हुन्छ । त्यसैले,
नोक्सान रकम = \(75,000 - 72,000 = 3,000\)
अब,
नोक्सान प्रतिशत = \( \dfrac{3,000}{75,000} \times 100\% = 4\% \)
तसर्थ, गणेशलाई ४% नोक्सान भयो ।

Question 24

Ram has a stationery shop at his house. He sells a calculator with a marked price Rs 450 at a discount of \(12\%\), and he sells a ball at Rs 850 after giving \(15\%\) discount.

If marked price (\(M\)) and discount (\(D\)) are given, then write the formula to find the price after discount.[1]
How much is the discount amount of the calculator? Find it.[1]
Find the marked price of the ball.[1]
By how much is the discount amount on the calculator more or less than the discount amount on the ball?[1]

Formula to find the price after discount:
Price after discount = \( M - D \)
or, if discount is given as a percentage \(D\%\):
Price after discount = \( (100-D)\% \times M \)
Discount amount of the calculator.
Marked Price (\(M\)) = Rs. \(450\)
Discount = \(12\%\)
Thus
Discount Amount = \( \dfrac{12}{100} \times 450 = 54 \)
So, the discount amount on the calculator is Rs. \(54\).
Marked price of the ball.
Selling Price (SP) = Rs. \(850\)
Discount = \(15\%\)
Thus
SP = 85% of Marked Price (MP)
or\(850 = \dfrac{85}{100} \times \text{MP}\)
or\(\text{MP} = \dfrac{850 \times 100}{85} = 1,000\)
So, the marked price of the ball is Rs. \(1,000\).
Difference between discount amounts.
Discount on calculator = Rs. \(54\) (from part ii)
Discount on ball = \(15\%\) of\(1,000 = \dfrac{15}{100} \times 1,000 = 150\)
Thus
Difference = \(150 - 54 = 96\)
So, the discount amount on the calculator is Rs. \(96\) less than that on the ball.

रामको घरमा एउटा स्टेसनरी पसल छ । उनले रु. ४५० अङ्कित मूल्य भएको क्याल्कुलेटर १२% छुटमा बेच्छन् र रु. ८५० मा १५% छुट दिएर एउटा बल बेच्छन् ।
1. यदि अङ्कित मूल्य (\(M\)) र छुट रकम (\(D\)) दिइएको छ भने, छुट पछिको मूल्य पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
2. क्याल्कुलेटरको छुट रकम कति हुन्छ ? पत्ता लगाउनुहोस् । [1]
3. बलको अङ्कित मूल्य पत्ता लगाउनुहोस् । [1]
4. क्याल्कुलेटरमा दिइएको छुट रकम बलमा दिइएको छुट रकमभन्दा कतिले कम वा बढी छ ? [1]

छुट पछिको मूल्य पत्ता लगाउने सूत्र:
छुट पछिको मूल्य = \( M - D \)
वा, यदि छुट प्रतिशत \(D\%\) मा दिइएको छ भने:
छुट पछिको मूल्य = \( (100-D)\% \times M \)
क्याल्कुलेटरको छुट रकम:
अङ्कित मूल्य (\(M\)) = रु. \(450\)
छुट प्रतिशत = १२%
यसरी,
छुट रकम = \( \dfrac{12}{100} \times 450 = 54 \)
तसर्थ, क्याल्कुलेटरमा दिइएको छुट रकम रु. ५४ हो ।
बलको अङ्कित मूल्य:
विक्रय मूल्य (SP) = रु. \(850\)
छुट प्रतिशत = १५%
यसरी,
विक्रय मूल्य (SP) = अङ्कित मूल्य (MP) को 85%
वा \(850 = \dfrac{85}{100} \times \text{MP}\)
वा \(\text{MP} = \dfrac{850 \times 100}{85} = 1,000\)
तसर्थ, बलको अङ्कित मूल्य रु. १,००० हो ।
छुट रकमहरू बीचको फरक:
क्याल्कुलेटरको छुट = रु. ५४ (भाग ii बाट)
बलको छुट = रु. \(1,000\) को १५% = \( \dfrac{15}{100} \times 1,000 = 150 \)
यसरी,
फरक = \(150 - 54 = 96\)
तसर्थ, क्याल्कुलेटरको छुट रकम बलको छुट रकमभन्दा रु. ९६ ले कम छ ।

Question 25

Ashok Mahato went to a stationery shop to buy a ball. He saw two balls \(A\) and \(B\) as shown in the figure. The ratio of marked prices of ball \(A\) and ball \(B\) is \(3:2\). The marked price of ball \(A\) is Rs 3750; the marked price of ball \(B\) is Rs 2500, and a \(5\%\) discount is offered.

⚽🏀

Write the marked prices of balls \(A\) and \(B\) in proportion.[1]
If Ashok Mahato decided to buy ball \(B\), what amount should he pay for it? Find it.[1]
If the shopkeeper earned \(25\%\) profit by selling ball \(B\) after the discount, at what price did he buy ball \(B\)?[2]

Marked prices of balls in proportion:
Marked Price of \(A\) : Marked Price of \(B\) = \(3750 : 2500\)
or\(3750 :1250 = 3: 2\)
Amount Ashok should pay for ball \(B\).
Marked Price of ball \(B\) = Rs. \(2,500\)
Discount = \(5\%\)
Thus
Selling Price = 95% of MP = \( \dfrac{95}{100} \times 2,500 = 2,375 \)
So, Ashok should pay Rs. \(2,375\) for ball \(B\).
Cost price of ball .
Selling Price = Rs. \(2,375\)
Profit = \(25\%\)
Thus
SP = 1250% of CP
or\(2,375 = \dfrac{125}{100} \times \text{CP}\)
or\(\text{CP} = \dfrac{2,375 \times 100}{125} = \dfrac{237,500}{125} =1900\)
So, the shopkeeper bought ball \(B\) for Rs. 1900.

अशोक महतो एउटा बल किन्न स्टेसनरी पसलमा गए । उनले चित्रमा देखाइए जस्तै दुईवटा बलहरू A र B देखे । बल A र बल B को अङ्कित मूल्यको अनुपात ३:२ छ । बल A को अङ्कित मूल्य रु. ३,७५० र बल B को अङ्कित मूल्य रु. २,५०० छ र यसमा ५% छुटको व्यवस्था छ ।
⚽🏀
1. बल A र B को अङ्कित मूल्यलाई अनुपात (Proportion) मा लेख्नुहोस् । [1]
2. यदि अशोक महतोले बल B किन्ने निर्णय गरे भने उनले कति रकम तिर्नुपर्ला ? पत्ता लगाउनुहोस् । [1]
3. यदि छुट दिएर बल B बेच्दा पसलेले २५% नाफा कमाएका भए, उनले बल B कतिमा किनेका थिए ? [2]

बलहरूको अङ्कित मूल्य अनुपातमा:
बल A को अङ्कित मूल्य : बल B को अङ्कित मूल्य = \(3750 : 2500\)
वा \(3750 : 2500 = 3: 2\)
अशोकले बल B को लागि तिर्नुपर्ने रकम:
बल B को अङ्कित मूल्य = रु. \(2,500\)
छुट = ५%
यसरी,
विक्रय मूल्य (SP) = अङ्कित मूल्यको 95% = \( \dfrac{95}{100} \times 2,500 = 2,375 \)
तसर्थ, अशोकले बल B को लागि रु. २,३७५ तिर्नुपर्छ ।
बल B को क्रय मूल्य:
विक्रय मूल्य (SP) = रु. २,३७५
नाफा = २५%
यसरी,
SP = CP को 125%
वा \(2,375 = \dfrac{125}{100} \times \text{CP}\)
वा \(\text{CP} = \dfrac{2,375 \times 100}{125} = \dfrac{237,500}{125} = 1900\)
तसर्थ, पसलेले बल B रु. १,९०० मा किनेका थिए ।

Question 26

Raju Lama visited a computer store to get \(5\) printers and a laptop. A set of \(5\) printers and a laptop is available for Rs 465000.

If \(15\%\) discount is allowed on those machineries, find the discount amount.[2]
If the shopkeeper earned \(20\%\) profit even after allowing \(15\%\) discount, at what price did the shopkeeper purchase such machineries?[2]
By how much is the marked price of a laptop less or more than Rs 95000, if the price of a printer is Rs 75000?[1]

Discount amount when \(15\%\) discount is allowed.
Marked Price (MP) of the set = Rs. \(465,000\)
Discount = \(15\%\)
Thus
Discount Amount = \( \dfrac{15}{100} \times 465,000 = 69,750 \)
So, the discount amount is Rs. \(69,750\).
Cost price of the machineries
Marked Price (MP) = Rs. \(465,000\)
Discount = \(15\%\)
Thus
Selling Price (SP) = 85% of MP = \( \dfrac{85}{100} \times 465,000 = 395,250 \)
Profit = \(20\%\)
Thus
SP = 120% of CP
or\(395,250 = \dfrac{120}{100} \times \text{CP}\)
or\(\text{CP} = \dfrac{395,250 \times 100}{120} = \dfrac{39,525,000}{120} = 329,375\)
So, the shopkeeper purchased the machineries for Rs. \(329,375\).
Difference between the laptop’s marked price .
Price of one printer = Rs. \(75,000\)
Price of 5 printers = \(5 \times 75,000 = 375,000\)
Total marked price of set = Rs. \(465,000\)
Thus
Marked Price of Laptop = \(465,000 - 375,000 = 90,000\)
Thus
\(95,000 - 90,000 = 5,000\)
Marked price of the laptop is Rs. 5,000 less than Rs. 95,000.

राजु लामा ५ वटा प्रिन्टर र एउटा ल्यापटप किन्न कम्प्युटर पसलमा गए । ५ वटा प्रिन्टर र एउटा ल्यापटपको सेटको मूल्य रु. ४,६५,००० तोकिएको छ ।
1. यदि ती सामानहरूमा १५% छुट दिइन्छ भने, छुट रकम पत्ता लगाउनुहोस् । [2]
2. यदि १५% छुट दिँदा पनि पसलेले २०% नाफा कमाएका रहेछन् भने, पसलेले ती सामानहरू कतिमा किनेका थिए ? [2]
3. यदि एउटा प्रिन्टरको मूल्य रु. ७५,००० भए, ल्यापटपको अङ्कित मूल्य रु. ९५,००० भन्दा कतिले बढी वा कम छ ? [1]

१५% छुट दिँदाको छुट रकम:
सामानहरूको अङ्कित मूल्य (MP) = रु. ४,६५,०००
छुट = १५%
यसरी,
छुट रकम = \( \dfrac{15}{100} \times 465,000 = 69,750 \)
तसर्थ, छुट रकम रु. ६९,७५० हो ।
सामानहरूको क्रय मूल्य:
अङ्कित मूल्य (MP) = रु. ४,६५,०००
छुट = १५%
यसरी,
विक्रय मूल्य (SP) = MP को 85% = \( \dfrac{85}{100} \times 465,000 = 395,250 \)
नाफा = २०%
हामीलाई थाहा छ,
SP = CP को 120%
वा \(395,250 = \dfrac{120}{100} \times \text{CP}\)
वा \(\text{CP} = \dfrac{395,250 \times 100}{120} = 329,375\)
तसर्थ, पसलेले ती सामानहरू रु. ३,२९,३७५ मा किनेका थिए ।
ल्यापटपको अङ्कित मूल्य बीचको फरक:
एउटा प्रिन्टरको मूल्य = रु. ७५,०००
५ वटा प्रिन्टरको मूल्य = \(5 \times 75,000 = 375,000\)
सेटको जम्मा अङ्कित मूल्य = रु. ४,६५,०००
यसरी,
ल्यापटपको अङ्कित मूल्य = \(465,000 - 375,000 = 90,000\)
अब,
\(95,000 - 90,000 = 5,000\)
तसर्थ, ल्यापटपको अङ्कित मूल्य रु. ९५,००० भन्दा रु. ५,००० ले कम छ ।

Question 27

The marked price of a television is Rs24000. If the shopkeeper got Rs2400 profit after selling it with \(15\%\) discount, then

If marked price and discount amount are represented by \(MP\) and \(D\) respectively, write the formula to find the selling price after discount.[1]
How much discount had been given by the shopkeeper to sell the television? Find it.[2]
Find the cost price of the television.[2]

Formula to find the selling price after discount:
Selling Price (SP) = MP – D
or, if discount is given as a percentage \(D\%\):
SP = \((100 -D)\% \times MP\)
Discount amount
Marked Price (MP) = Rs. \(24,000\)
Discount = \(15\%\)
Thus
Discount = \( \dfrac{15}{100} \times 24,000 = 3,600 \)
So, the discount given was Rs. \(3,600\).
Cost price of the television.
Marked Price (MP) = Rs. \(24,000\)
Discount = \(15\%\)
Thus
Selling Price (SP) = 85% of MP = \( \dfrac{85}{100} \times 24,000 = 20,400 \)
Profit = Rs. \(2,400\)
We know that
CP = SP – Profit=\(20,400 - 2,400 = 18,000\)
So, the cost price of the television was Rs. \(18,000\).

एउटा टेलिभिजनको अङ्कित मूल्य रु. २४,००० छ । यदि पसलेले १५% छुट दिएर उक्त टेलिभिजन बेच्दा रु. २,४०० नाफा कमाएका रहेछन् भने:
1. यदि अङ्कित मूल्य र छुट रकमलाई क्रमशः \(MP\) र \(D\) ले जनाइन्छ भने, छुट पछिको विक्रय मूल्य पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
2. टेलिभिजन बेच्दा पसलेले जम्मा कति छुट दिएका थिए ? पत्ता लगाउनुहोस् । [2]
3. टेलिभिजनको क्रय मूल्य पत्ता लगाउनुहोस् । [2]

छुट पछिको विक्रय मूल्य पत्ता लगाउने सूत्र:
विक्रय मूल्य (SP) = MP – D
वा, यदि छुट प्रतिशत \(D\%\) मा दिइएको छ भने:
SP = \((100 - D)\% \times MP\)
छुट रकम:
अङ्कित मूल्य (MP) = रु. २४,०००
छुट = १५%
यसरी,
छुट रकम = \( \dfrac{15}{100} \times 24,000 = 3,600 \)
तसर्थ, पसलेले रु. ३,६०० छुट दिएका थिए ।
टेलिभिजनको क्रय मूल्य:
अङ्कित मूल्य (MP) = रु. २४,०००
छुट = १५%
यसरी,
विक्रय मूल्य (SP) = MP को 85% = \( \dfrac{85}{100} \times 24,000 = 20,400 \)
नाफा = रु. २,४००
हामीलाई थाहा छ,
क्रय मूल्य (CP) = SP – नाफा = \(20,400 - 2,400 = 18,000\)
तसर्थ, टेलिभिजनको क्रय मूल्य रु. १८,००० थियो ।

Question 28

Ashim bought a machine for Rs 25,000 and fixed the marked price by increasing the cost price by 20%. He incurred a loss of Rs 1,000 after selling the machine with some discount.
1. Find the marked price of the machine. [1]
2. At what discount percentage was the machine sold? Find it. [2]
3. If Ashim wants to earn a profit of Rs 2,000 by selling the machine, what discount rate should be maintained? [1]

Finding the marked price of the machine
Cost price (CP) = Rs.\(25,000\)
Percentage increase to fix marked price (MP) = 20%
Therefore, the marked price is
Marked Price (MP) = 120% of CP
orMarked Price (MP) =\( \frac{120}{100} \times 25,000 \)
orMarked Price (MP) = 30,000
So, the marked price of the machine is Rs.\(30,000\).
Finding the discount percentage
Ashim sold the machine at a loss of Rs.\(1,000\).
So, Selling Price (SP) = CP - Loss = 25,000 - 1,000 = 24,000
Now
Discount % = \(\frac{MP - SP}{MP} \times 100\%= \frac{30,000 - 24,000}{30,000} \times 100\%\)
or Discount% =\( \frac{6,000}{30,000} \times 100\%=20\%\)
So, the machine was sold at 20% discount.
Finding the discount rate to earn Rs.\(2,000\) profit
Desired profit = Rs.\(2,000\)
So, Selling Price (SP) = CP + Profit = 25,000 + 2,000 = 27,000
Now
Discount% =\(\frac{MP - SP}{MP} \times 100\%= \frac{30,000 - 27,000}{30,000} \times 100\%\)
or Discount% =\( \frac{3,000}{30,000} \times 100\%=10\%\)
So, to earn a profit of Rs.\(2,000\), Ashim should give a 10% discount.

अशिमले एउटा मेसिन रु. २५,००० मा किनेको थियो र यसको मूल्यमा २०% बढाएर बजार मूल्य तोकेको थियो। उसले केही छुट दिएर मेसिन बेचेपछि रु. १,००० को नोक्सानी भयो।
1. मेसिनको अङ्कित मूल्य पत्ता लगाउनुहोस्। [१]
2. मेसिन कति प्रतिशत छुटमा बेचिएको थियो? पत्ता लगाउनुहोस्। [२]
3. यदि अशिमले मेसिन बेचेर रु. २,००० को नाफा कमाउन चाहन्छ भने, कति छुट दर कायम गर्नुपर्छ? [१]

मेसिनको अङ्कित मूल्य निकाल्ने तरिका:
क्रय मूल्य (CP) = रु. \(25,000\)
मूल्य वृद्धि प्रतिशत = \(20\%\)
अङ्कित मूल्य (MP) = CP को \(120\%\)
वाMP = \( \dfrac{120}{100} \times 25,000 = 30,000 \)
तसर्थ, मेसिनको अङ्कित मूल्य रु. \(30,000\) हो ।
छुट प्रतिशत निकाल्ने तरिका:
अशिमले रु. \(1,000\) नोक्सानमा मेसिन बेचेका छन् ।
विक्रय मूल्य (SP) = CP – नोक्सान = \(25,000 - 1,000 = 24,000\)
अब,
छुट% = \( \dfrac{MP - SP}{MP} \times 100\% = \dfrac{30,000 - 24,000}{30,000} \times 100\% \)
वाछुट% = \( \dfrac{6,000}{30,000} \times 100\% = 20\% \)
तसर्थ, मेसिन \(20\%\) छुटमा बेचिएको थियो ।
रु. \(2,000\) नाफा कमाउन चाहिने छुट दर निकाल्ने तरिका:
चाहिएको नाफा = रु. \(2,000\)
नयाँ विक्रय मूल्य (SP) = CP + नाफा = \(25,000 + 2,000 = 27,000\)
अब,
छुट% = \( \dfrac{MP - SP}{MP} \times 100\% = \dfrac{30,000 - 27,000}{30,000} \times 100\% \)
वाछुट% = \( \dfrac{3,000}{30,000} \times 100\% = 10\% \)
तसर्थ, रु. \(2,000\) नाफा कमाउन अशिमले \(10\%\) छुट दर कायम गर्नुपर्छ ।

Question 29

The cost price of a mobile is Rs. \(21,000\) and the marked price is \(30\%\) above the cost price.
1. Write the formula to find profit percent. [1]
2. Find the marked price. [1]
3. If the mobile phone was sold for Rs. \(24,024\), find the discount amount. [1]

Formula to find profit percent is
Profit Percent = \( \dfrac{\text{Profit}}{\text{CP}} \times 100\% \)
orProfit Percent = \( \dfrac{\text{SP} - \text{CP}}{\text{CP}} \times 100\% \)
Finding the marked price
Cost Price (CP) = Rs. \(21,000\)
Marked Price is \(30\%\) above CP.
Therefore
Marked Price (MP) = \(130\%\) of CP
orMP = \( \dfrac{130}{100} \times 21,000 = 27,300 \)
So, the marked price is Rs. \(27,300\).
Finding the discount amount
Selling Price (SP) = Rs. \(24,024\)
Marked Price (MP) = Rs. \(27,300\)
Discount = MP – SP
orDiscount = \(27,300 - 24,024 = 3,276\)
So, the discount amount is Rs. \(3,276\).

एउटा मोबाइलको क्रय मूल्य रु. \(21,000\) र अङ्कित मूल्य क्रय मूल्यभन्दा \(30\%\) ले बढी छ ।
1. नाफा प्रतिशत निकाल्ने सूत्र लेख्नुहोस् । [१]
2. अङ्कित मूल्य पत्ता लगाउनुहोस् । [१]
3. उक्त मोबाइल रु. \(24,024\) मा बेचिएको भए छुट रकम पत्ता लगाउनुहोस् । [१]

नाफा प्रतिशत निकाल्ने सूत्र निम्न अनुसार छ:
नाफा प्रतिशत = \( \dfrac{\text{Profit}}{\text{CP}} \times 100\% \)
वानाफा प्रतिशत = \( \dfrac{\text{SP} - \text{CP}}{\text{CP}} \times 100\% \)
अङ्कित मूल्य निकाल्ने तरिका:
क्रय मूल्य (CP) = रु. \(21,000\)
अङ्कित मूल्य क्रय मूल्यभन्दा \(30\%\) ले बढी छ ।
त्यसैले,
अङ्कित मूल्य (MP) = क्रय मूल्यको \(130\%\)
वाMP = \( \dfrac{130}{100} \times 21,000 = 27,300 \)
तसर्थ, अङ्कित मूल्य रु. \(27,300\) हो ।
छुट रकम पत्ता लगाउने तरिका:
विक्रय मूल्य (SP) = रु. \(24,024\)
अङ्कित मूल्य (MP) = रु. \(27,300\)
छुट रकम = अङ्कित मूल्य – विक्रय मूल्य
वाछुट रकम = \(27,300 - 24,024 = 3,276\)
तसर्थ, छुट रकम रु. \(3,276\) हो ।

Question 30

A laptop costing Rs. \(45,000\) is sold at a discount of \(20\%\).
1. Write the formula to find discount percent. [1K]
2. Find the discount amount. [1U]
3. If the laptop is sold at a loss of \(10\%\), find the cost price. [2A]

Formula to find discount percent is
Discount Percent = \( \dfrac{\text{Discount Amount}}{\text{Marked Price}} \times 100\% \)
orDiscount Percent = \( \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
Finding the discount amount
Marked Price (MP) = Rs. \(45,000\)
Discount Percent = \(20\%\)
Therefore,
Discount Amount = \(20\%\) of MP
orDiscount Amount = \( \dfrac{20}{100} \times 45,000 = 9,000 \)
So, the discount amount is Rs. \(9,000\).
Finding the cost price when sold at \(10\%\) loss
Selling Price (SP) = Marked Price – Discount = \(45,000 - 9,000 = 36,000\)
Loss Percent = \(10\%\)
We know that,
SP = \(90\%\) of CP
So,
\(36,000 = \dfrac{90}{100} \times \text{CP}\)
or\(\text{CP} = \dfrac{36,000 \times 100}{90} = 40,000\)
Hence, the cost price of the laptop is Rs. \(40,000\).

रु. \(45,000\) पर्ने एउटा ल्यापटप \(20\%\) छुटमा बेचिएको छ ।
1. छुट प्रतिशत पत्ता लगाउने सूत्र लेख्नुहोस् । [१K]
2. छुट रकम पत्ता लगाउनुहोस् । [१U]
3. उक्त ल्यापटप \(10\%\) घाटामा बेचिएको रहेछ भने क्रय मूल्य पत्ता लगाउनुहोस् । [२A]

छुट प्रतिशत निकाल्ने सूत्र निम्न अनुसार छ:
छुट प्रतिशत = \( \dfrac{\text{Discount}}{\text{MP}} \times 100\% \)
वाDiscount Percent = \( \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
छुट रकम निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(45,000\)
छुट प्रतिशत = \(20\%\)
त्यसैले,
छुट रकम = अङ्कित मूल्यको \(20\%\)
वाछुट रकम = \( \dfrac{20}{100} \times 45,000 = 9,000 \)
तसर्थ, छुट रकम रु. \(9,000\) हो ।
\(10\%\) घाटामा बेचिएको अवस्थामा क्रय मूल्य निकाल्ने तरिका:
विक्रय मूल्य (SP) = अङ्कित मूल्य – छुट रकम = \(45,000 - 9,000 = 36,000\)
घाटा प्रतिशत = \(10\%\)
हामीलाई थाहा छ,
SP = CP को \(90\%\)
त्यसैले,
\(36,000 = \dfrac{90}{100} \times \text{CP}\)
वा\(\text{CP} = \dfrac{36,000 \times 100}{90} = 40,000\)
तसर्थ, ल्यापटपको क्रय मूल्य रु. \(40,000\) हो ।

Question 31

Santaram bought a fan of level price Rs. \(1800\) at \(20\%\) discount.
1. How much is the selling price of an article whose marked price is \(MP\) and the discount percent is \(D\%\)? [1K]
2. Find the selling price of the fan. [1U]
3. If the fan is sold at \(10\%\) loss, find the cost price. [2A]

The selling price (SP) of an article with marked price \(MP\) and discount percent \(D\%\) is given by:
Selling Price (SP) = \( MP - \dfrac{D}{100} \times MP \)
orSelling Price (SP) = \( (100-D)\% \times MP \)
Finding the selling price of the fan
Marked Price (MP) = Rs. \(1800\)
Discount Percent = \(20\%\)
Therefore,
\(SP = 80\% \times 1800 = 1440\)
So, the selling price of the fan is Rs. \(1440\).
Finding the cost price when sold at \(10\%\) loss
Selling Price (SP) = Rs. \(1440\)
Loss Percent = \(10\%\)
We know that,
SP = \(90\%\) of CP
So,
\(1440 = \dfrac{90}{100} \times \text{CP}\)
or\(\text{CP} = \dfrac{1440 \times 100}{90} = 1600\)
Hence, the cost price of the fan is Rs. \(1600\).

सन्तरामले अङ्कित मूल्य रु. \(1800\) भएको एउटा पङ्खा \(20\%\) छुटमा किनेछन् ।
1. छुट प्रतिशत (\(D\%\)) र अङ्कित मूल्य (\(MP\)) भएको सामानको विक्रय मूल्य कति हुन्छ ? [१K]
2. उक्त पङ्खाको विक्रय मूल्य पत्ता लगाउनुहोस् । [१U]
3. उक्त पङ्खा \(10\%\) नोक्सानमा बेचिएको रहेछ भने क्रय मूल्य पत्ता लगाउनुहोस् । [२A]

अङ्कित मूल्य \(MP\) र छुट प्रतिशत \(D\%\) भएको सामानको विक्रय मूल्य (SP) निकाल्ने सूत्र निम्न अनुसार छ:
विक्रय मूल्य (SP) = \( MP - \dfrac{D}{100} \times MP \)
वाविक्रय मूल्य (SP) = \( (100-D)\% \times MP \)
पङ्खाको विक्रय मूल्य निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(1800\)
छुट प्रतिशत = \(20\%\)
त्यसैले,
\(SP = 1800 \text{ को } 80\% = 1440\)
तसर्थ, पङ्खाको विक्रय मूल्य रु. \(1440\) हो ।
\(10\%\) नोक्सानमा बेचिएको अवस्थामा क्रय मूल्य निकाल्ने तरिका:
विक्रय मूल्य (SP) = रु. \(1440\)
नोक्सान प्रतिशत = \(10\%\)
हामीलाई थाहा छ,
SP = CP को \(90\%\)
त्यसैले,
\(1440 = \dfrac{90}{100} \times \text{CP}\)
वा\(\text{CP} = \dfrac{1440 \times 100}{90} = 1600\)
तसर्थ, पङ्खाको क्रय मूल्य रु. \(1600\) हो ।

Question 32

A mobile set of marked price Rs. \(25,000\) is sold on a discount of \(10\%\).
1. Write the formula to find the selling price (\(SP\)) when discount percent (\(D\%\)) and the marked price (\(MP\)) are given. [1K]
2. Find the selling price of the mobile. [1U]
3. If the cost price of the mobile is Rs. \(20,000\), find the profit percent. [2A]

The formula to find the selling price (\(SP\)) when marked price (\(MP\)) and discount percent (\(D\%\)) are given is:
\( SP = MP - \dfrac{D}{100} \times MP \)
or\( SP = (100-D)\% \times MP \)
Finding the selling price of the mobile
Marked Price (MP) = Rs. \(25,000\)
Discount Percent = \(10\%\)
Therefore,
\( SP = 90\% \times 25,000 = 22,500 \)
So, the selling price of the mobile is Rs. \(22,500\).
Finding the profit percent
Cost Price (CP) = Rs. \(20,000\)
Selling Price (SP) = Rs. \(22,500\)
Profit = SP – CP = \(22,500 - 20,000 = 2,500\)
Now,
Profit Percent = \( \dfrac{\text{Profit}}{\text{CP}} \times 100\% = \dfrac{2,500}{20,000} \times 100\% \)
orProfit Percent = \(12.5\% \)
Hence, the profit percent is \(12.5\%\).

अङ्कित मूल्य रु. \(25,000\) भएको एउटा मोबाइल \(10\%\) छुटमा बेचिएछ ।
1. छुट प्रतिशत (\(D\%\)) र अङ्कित मूल्य (\(MP\)) दिइएको अवस्थामा विक्रय मूल्य (\(SP\)) पत्ता लगाउने सूत्र लेख्नुहोस् । [१K]
2. उक्त मोबाइलको विक्रय मूल्य पत्ता लगाउनुहोस् । [१U]
3. उक्त मोबाइलको क्रय मूल्य रु. \(20,000\) भए नाफा प्रतिशत पत्ता लगाउनुहोस् । [२A]

अङ्कित मूल्य (\(MP\)) र छुट प्रतिशत (\(D\%\)) दिइएको अवस्थामा विक्रय मूल्य (\(SP\)) निकाल्ने सूत्र निम्न अनुसार छ:
\( SP = MP - \dfrac{D}{100} \times MP \)
वा\( SP = (100-D)\% \times MP \)
मोबाइलको विक्रय मूल्य निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(25,000\)
छुट प्रतिशत = \(10\%\)
त्यसैले,
\( SP = 25,000 \times 90\% = 22,500 \)
तसर्थ, मोबाइलको विक्रय मूल्य रु. \(22,500\) हो ।
नाफा प्रतिशत निकाल्ने तरिका:
क्रय मूल्य (CP) = रु. \(20,000\)
विक्रय मूल्य (SP) = रु. \(22,500\)
नाफा = विक्रय मूल्य – क्रय मूल्य = \(22,500 - 20,000 = 2,500\)
अब,
नाफा प्रतिशत = \( \dfrac{\text{Profit}}{\text{CP}} \times 100\% = \dfrac{2,500}{20,000} \times 100\% \)
वानाफा प्रतिशत = \(12.5\% \)
तसर्थ, नाफा प्रतिशत \(12.5\%\) हो ।

Question 33

A book with marked price Rs. \(750\) is sold for Rs. \(600\).
1. What is meant by discount percent? Write it. [1K]
2. Find the discount percent. [1U]
3. If the book is sold with \(13\%\) value added tax (\(VAT\)), find the price with \(VAT\). [2A]

Discount percent is the percentage of the marked price that is reduced or given as a concession to the customer while selling the article. It is always calculated on the marked price (MP).
Finding the discount percent
Marked Price (MP) = Rs. \(750\)
Selling Price (SP) = Rs. \(600\)
Discount Amount = MP – SP = \(750 - 600 = 150\)
Now,
Discount Percent = \( \dfrac{\text{Discount}}{\text{MP}} \times 100\% = \dfrac{150}{750} \times 100\% = 20\% \)
So, the discount percent is \(20\%\).
Finding the price with \(13\%\) VAT
Selling Price (before VAT) = Rs. \(600\)
VAT Percent = \(13\%\)
Price with VAT = \(113\%\) of \(600 = \dfrac{113}{100} \times 600 = 678\)
Hence, the price of the book including \(13\%\) VAT is Rs. \(678\).

अङ्कित मूल्य रु. \(750\) भएको एउटा पुस्तक रु. \(600\) मा बेचिएछ ।
1. छुट प्रतिशत भन्नाले के बुझिन्छ ? लेख्नुहोस् । [१K]
2. छुट प्रतिशत पत्ता लगाउनुहोस् । [१U]
3. उक्त पुस्तक \(13\%\) मूल्य अभिवृद्धि कर (\(VAT\)) लगाएर बेच्दा मूल्य कति पर्छ ? [२A]

छुट प्रतिशत भन्नाले सामान बिक्री गर्दा अङ्कित मूल्यमा ग्राहकलाई दिइने सहुलियत वा घटाइएको रकमको प्रतिशतलाई बुझिन्छ । यो सधैँ अङ्कित मूल्य (MP) मा गणना गरिन्छ ।
छुट प्रतिशत निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(750\)
विक्रय मूल्य (SP) = रु. \(600\)
छुट रकम = MP – SP = \(750 - 600 = 150\)
अब,
छुट प्रतिशत = \( \dfrac{\text{Discount}}{\text{MP}} \times 100\% = \dfrac{150}{750} \times 100\% = 20\% \)
तसर्थ, छुट प्रतिशत \(20\%\) हो ।
\(13\%\) VAT सहितको मूल्य निकाल्ने तरिका:
विक्रय मूल्य (VAT बाहेक) = रु. \(600\)
VAT प्रतिशत = \(13\%\)
VAT सहितको मूल्य = \(600\) को \(113\% = \dfrac{113}{100} \times 600 = 678\)
तसर्थ, \(13\%\) VAT सहितको पुस्तकको मूल्य रु. \(678\) हो ।

Question 34

A television with marked price Rs. \(70,000\) is sold at a discount of \(20\%\).
1. Write the selling price (\(SP\)) in terms of marked price (\(MP\)) and discount percent. [1K]
2. Find the selling price. [1U]
3. Find the cost price of the television if there is \(12\%\) profit.[2A]

The selling price (\(SP\)) in terms of marked price (\(MP\)) and discount percent (\(D\%\)) is:
\( SP = MP - \dfrac{D}{100} \times MP \)
or\( SP = (100-D)\% \times MP \)
Finding the selling price of the television
Marked Price (MP) = Rs. \(70,000\)
Discount Percent = \(20\%\)
Therefore,
\( SP = 80\% \times 70,000 = 0.8 \times 70,000 = 56,000 \)
So, the selling price of the television is Rs. \(56,000\).
Finding the cost price when profit is \(12\%\)
Selling Price (SP) = Rs. \(56,000\)
Profit Percent = \(12\%\)
We know that,
SP = \(112\%\) of CP
So,
\(56,000 = \dfrac{112}{100} \times \text{CP}\)
or\(\text{CP} = \dfrac{56,000 \times 100}{112} = 50,000\)
Hence, the cost price of the television is Rs. \(50,000\).

अङ्कित मूल्य रु. \(70,000\) भएको एउटा टेलिभिजन \(20\%\) छुटमा बेचिएछ ।
1. विक्रय मूल्य (\(SP\)) लाई अङ्कित मूल्य (\(MP\)) र छुट प्रतिशतको रूपमा लेख्नुहोस् । [१K]
2. उक्त टेलिभिजनको विक्रय मूल्य पत्ता लगाउनुहोस् । [१U]
3. उक्त टेलिभिजनमा \(12\%\) नाफा भएको भए क्रयमूल्य पत्ता लगाउनुहोस् । [२A]

विक्रय मूल्य (\(SP\)) लाई अङ्कित मूल्य (\(MP\)) र छुट प्रतिशत (\(D\%\)) को रूपमा निम्न अनुसार लेखिन्छ:
\( SP = MP - \dfrac{D}{100} \times MP \)
वा\( SP = (100-D)\% \times MP \)
टेलिभिजनको विक्रय मूल्य निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(70,000\)
छुट प्रतिशत = \(20\%\)
त्यसैले,
\( SP = 70,000 \times 80\% = 0.8 \times 70,000 = 56,000 \)
तसर्थ, टेलिभिजनको विक्रय मूल्य रु. \(56,000\) हो ।
\(12\%\) नाफा भएको अवस्थामा क्रय मूल्य निकाल्ने तरिका:
विक्रय मूल्य (SP) = रु. \(56,000\)
नाफा प्रतिशत = \(12\%\)
हामीलाई थाहा छ,
SP = CP को \(112\%\)
त्यसैले,
\(56,000 = \dfrac{112}{100} \times \text{CP}\)
वा\(\text{CP} = \dfrac{56,000 \times 100}{112} = 50,000\)
तसर्थ, टेलिभिजनको क्रय मूल्य रु. \(50,000\) हो ।

Question 35

When a motorcycle is sold for \(20\%\) discount, it costs Rs. \(1,20,000\).
1. Write the formula to find the discount percent. [1K]
2. Find the marked price of the motorcycle. [2U]
3. If the cost price of the motorcycle is Rs. \(1,25,000\), find the loss percent. [2A]

The formula to find discount percent is:
Discount Percent = \( \dfrac{\text{Marked Price} - \text{Selling Price}}{\text{Marked Price}} \times 100\% \)
orDiscount Percent = \( \dfrac{\text{Discount Amount}}{\text{MP}} \times 100\% \)
Finding the marked price of the motorcycle
Selling Price (SP) = Rs. \(1,20,000\)
Discount Percent = \(20\%\)
We know that,
SP = \(80\%\) of MP
or\(1,20,000 = \dfrac{80}{100} \times \text{MP}\)
or\(\text{MP} = \dfrac{1,20,000 \times 100}{80} = 1,50,000\)
So, the marked price of the motorcycle is Rs. \(1,50,000\).
Finding the loss percent
Cost Price (CP) = Rs. \(1,25,000\)
Selling Price (SP) = Rs. \(1,20,000\)
Loss = CP – SP = \(1,25,000 - 1,20,000 = 5,000\)
Now,
Loss Percent = \( \dfrac{\text{Loss}}{\text{CP}} \times 100\% = \dfrac{5,000}{1,25,000} \times 100\% = 4\%\)
Hence, the loss percent is \(4\%\).

\(20\%\) छुटमा किन्दा एउटा मोटरसाइकलको मूल्य रु. \(1,20,000\) पर्छ ।
1. छुट प्रतिशत निकाल्ने सूत्र लेख्नुहोस् । [१K]
2. उक्त मोटरसाइकलको अङ्कित मूल्य पत्ता लगाउनुहोस् । [२U]
3. उक्त मोटरसाइकलको क्रय मूल्य रु. \(1,25,000\) भए नोक्सान प्रतिशत पत्ता लगाउनुहोस् । [२A]

छुट प्रतिशत निकाल्ने सूत्र निम्न अनुसार छ:
छुट प्रतिशत = \( \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
वाछुट प्रतिशत = \( \dfrac{\text{Discount}}{\text{MP}} \times 100\% \)
मोटरसाइकलको अङ्कित मूल्य निकाल्ने तरिका:
विक्रय मूल्य (SP) = रु. \(1,20,000\)
छुट प्रतिशत = \(20\%\)
हामीलाई थाहा छ,
विक्रय मूल्य (SP) = अङ्कित मूल्य (MP) को \(80\%\)
वा\(1,20,000 = \dfrac{80}{100} \times \text{MP}\)
वा\(\text{MP} = \dfrac{1,20,000 \times 100}{80} = 1,50,000\)
तसर्थ, मोटरसाइकलको अङ्कित मूल्य रु. \(1,50,000\) हो ।
नोक्सान प्रतिशत निकाल्ने तरिका:
क्रय मूल्य (CP) = रु. \(1,25,000\)
विक्रय मूल्य (SP) = रु. \(1,20,000\)
नोक्सान = क्रय मूल्य – विक्रय मूल्य = \(1,25,000 - 1,20,000 = 5,000\)
अब,
नोक्सान प्रतिशत = \( \dfrac{\text{Loss}}{\text{CP}} \times 100\% = \dfrac{5,000}{1,25,000} \times 100\% = 4\%\)
तसर्थ, नोक्सान प्रतिशत \(4\%\) हो ।

Question 36

In a shop in New Road, a mobile set with marked price Rs. \(40,000\) was sold for Rs. \(35,000\).
1. How much was the discount amount? Find it. [1K]
2. What was the percent of discount allowed? Find it. [1U]
3. Find the selling price of the mobile without \(VAT\) if it was sold for Rs. \(39,550\) with \(13\%\) \(VAT\). [2A]

Finding the discount amount
Marked Price (MP) = Rs. \(40,000\)
Selling Price (SP) = Rs. \(35,000\)
Discount Amount = MP – SP = \(40,000 - 35,000 = 5,000\)
So, the discount amount is Rs. \(5,000\).
Finding the discount percent
Discount Amount = Rs. \(5,000\)
Marked Price (MP) = Rs. \(40,000\)
Discount Percent = \( \dfrac{5,000}{40,000} \times 100\% = 12.5\% \)
So, the discount percent is \(12.5\%\).
Finding the selling price without VAT
Price including VAT (ASP) = Rs. \(39,550\)
VAT Percent = \(13\%\)
Let the selling price without VAT be \(SP\).
Then,
\(ASP = 113\% \times SP \)
or\(39,550 = 1.13 \times SP\)
or\(SP = \dfrac{39,550}{1.13} = 35,000\)
Hence, the selling price of the mobile without VAT is Rs. \(35,000\).

नयाँ सडकको एउटा पसलमा अङ्कित मूल्य रु. \(40,000\) भएको एउटा मोबाइल सेट रु. \(35,000\) मा बेचिएछ ।
1. छुट दिइएको रकम कति रहेछ ? पत्ता लगाउनुहोस् । [१K]
2. कति प्रतिशत छुट दिइएको रहेछ ? पत्ता लगाउनुहोस् । [१U]
3. \(13\%\) \(VAT\) सहित उक्त मोबाइल रु. \(39,550\) मा बेचिएको रहेछ भने \(VAT\) बिनाको विक्रय मूल्य पत्ता लगाउनुहोस् । [२A]

छुट रकम निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(40,000\)
विक्रय मूल्य (SP) = रु. \(35,000\)
छुट रकम = अङ्कित मूल्य – विक्रय मूल्य = \(40,000 - 35,000 = 5,000\)
तसर्थ, छुट रकम रु. \(5,000\) हो ।
छुट प्रतिशत निकाल्ने तरिका:
छुट रकम = रु. \(5,000\)
अङ्कित मूल्य (MP) = रु. \(40,000\)
छुट प्रतिशत = \( \dfrac{5,000}{40,000} \times 100\% = 12.5\% \)
तसर्थ, छुट प्रतिशत \(12.5\%\) हो ।
VAT बिनाको विक्रय मूल्य निकाल्ने तरिका:
VAT सहितको मूल्य (ASP) = रु. \(39,550\)
VAT प्रतिशत = \(13\%\)
मानाौँ, VAT बिनाको विक्रय मूल्य \(SP\) हो ।
तब,
\(ASP = SP \times 113\% \)
वा\(39,550 = 1.13 \times SP\)
वा\(SP = \dfrac{39,550}{1.13} = 35,000\)
तसर्थ, VAT बिनाको मोबाइलको विक्रय मूल्य रु. \(35,000\) हो ।

Question 37

Ramlal went to a shop to buy a gas stove. He bought a gas stove at \(10\%\) discount whose marked price was Rs. \(4200\).
1. Write the formula to find discount percent. [1K]
2. How much discount did he get while buying the stove? [1U]
3. While selling that stove the shopkeeper had \(5.5\%\) loss, find the cost price of the stove. [2A]

The formula to find discount percent is:
Discount Percent = \( \dfrac{\text{Discount Amount}}{\text{Marked Price}} \times 100\% \)
orDiscount Percent = \( \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
Finding the discount amount Ramlal received
Marked Price (MP) = Rs. \(4200\)
Discount Percent = \(10\%\)
Discount Amount = \(10\%\) of \(4200 = \dfrac{10}{100} \times 4200 = 420\)
So, Ramlal got a discount of Rs. \(420\).
Finding the cost price of the stove for the shopkeeper
Selling Price (SP) = MP – Discount = \(4200 - 420 = 3780\)
Loss Percent = \(5.5\%\)
We know that,
SP = \(94.5\%\) of CP
So,
\(3780 = \dfrac{94.5}{100} \times \text{CP}\)
or\(\text{CP} = \dfrac{3780 \times 100}{94.5} = 4000\)
Hence, the cost price of the stove for the shopkeeper was Rs. \(4000\).

रामलाल एउटा ग्यास चुलो किन्न एउटा पसलमा गएछन् । उसले अङ्कित मूल्य रु. \(4200\) भएको चुलो \(10\%\) छुटमा किनेछन् ।
1. छुट प्रतिशत निकाल्ने सूत्र लेख्नुहोस् । [१K]
2. उक्त चुलो किन्दा कति छुट पाएछन् ? [१U]
3. उक्त चुलो बेच्दा पसलेलाई \(5.5\%\) नोक्सान भएको रहेछ भने उक्त चुलोको क्रय मूल्य पत्ता लगाउनुहोस् । [२A]

छुट प्रतिशत निकाल्ने सूत्र निम्न अनुसार छ:
छुट प्रतिशत = \( \dfrac{\text{Discount}}{\text{MP}} \times 100\% \)
वाDiscount Percent = \( \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
रामलालले पाएको छुट रकम निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(4200\)
छुट प्रतिशत = \(10\%\)
छुट रकम = \(4200\) को \(10\%\) = \( \dfrac{10}{100} \times 4200 = 420 \)
तसर्थ, रामलालले रु. \(420\) छुट पाएछन् ।
पसलेको लागि चुलोको क्रय मूल्य निकाल्ने तरिका:
विक्रय मूल्य (SP) = अङ्कित मूल्य – छुट रकम = \(4200 - 420 = 3780\)
नोक्सान प्रतिशत = \(5.5\%\)
हामीलाई थाहा छ,
विक्रय मूल्य (SP) = क्रय मूल्य (CP) को \(94.5\%\)
त्यसैले,
\(3780 = \dfrac{94.5}{100} \times \text{CP}\)
वा\(\text{CP} = \dfrac{3780 \times 100}{94.5} = 4000\)
तसर्थ, पसलेको लागि उक्त चुलोको क्रय मूल्य रु. \(4000\) थियो ।

Question 38

Rajan bought a sweater for Rs. \(1075\) at a discount of \(14\%\).
1. What is called the difference between marked price and selling price? [1K]
2. Find the marked price of the sweater. [1U]
3. Find the cost price when sold at \(7.5\%\) profit

The difference between marked price (MP) and selling price (SP) is called the "discount amount".
Finding the marked price of the sweater
Selling Price (SP) = Rs. \(1075\)
Discount Percent = \(14\%\)
We know that,
\(SP = 86\%\) of MP
or\(1075 = \dfrac{86}{100} \times \text{MP}\)
or\(\text{MP} = \dfrac{1075 \times 100}{86} = 1250\)
So, the marked price of the sweater is Rs. \(1250\).
Finding the cost price when sold at \(7.5\%\) profit
Selling Price (SP) = Rs. \(1075\)
Profit Percent = \(7.5\%\)
We know that,
SP = \(107.5\%\) of CP So,
\(1075 = \dfrac{107.5}{100} \times \text{CP}\)
or\(\text{CP} = \dfrac{1075 \times 100}{107.5} = 1000\)
Hence, the cost price of the sweater is Rs. \(1000\).

राजनले \(14\%\) छुटमा एउटा स्वेटर किन्दा रु. \(1075\) तिरेछन् ।
1. अङ्कित मूल्य र विक्रय मूल्यको अन्तरलाई के भनिन्छ ? [१K]
2. उक्त स्वेटरको अङ्कित मूल्य पत्ता लगाउनुहोस् । [१U]
3. उक्त स्वेटर \(7.5\%\) नाफामा बेचिएको रहेछ भने क्रय मूल्य पत्ता लगाउनुहोस् । [२A]

अङ्कित मूल्य (MP) र विक्रय मूल्य (SP) बीचको अन्तरलाई "छुट रकम" (Discount Amount) भनिन्छ ।
स्वेटरको अङ्कित मूल्य निकाल्ने तरिका:
विक्रय मूल्य (SP) = रु. \(1075\)
छुट प्रतिशत = \(14\%\)
हामीलाई थाहा छ,
विक्रय मूल्य (SP) = अङ्कित मूल्य (MP) को \(86\%\)
वा\(1075 = \dfrac{86}{100} \times \text{MP}\)
वा\(\text{MP} = \dfrac{1075 \times 100}{86} = 1250\)
तसर्थ, स्वेटरको अङ्कित मूल्य रु. \(1250\) हो ।
\(7.5\%\) नाफा भएको अवस्थामा क्रय मूल्य निकाल्ने तरिका:
विक्रय मूल्य (SP) = रु. \(1075\)
नाफा प्रतिशत = \(7.5\%\)
हामीलाई थाहा छ,
विक्रय मूल्य (SP) = क्रय मूल्य (CP) को \(107.5\%\)
त्यसैले,
\(1075 = \dfrac{107.5}{100} \times \text{CP}\)
वा\(\text{CP} = \dfrac{1075 \times 100}{107.5} = 1000\)
तसर्थ, स्वेटरको क्रय मूल्य रु. \(1000\) हो ।

Question 39

Sita bought a mobile at Rs. \(24,000\). She has bought at \(20\%\) discount.
1. Write the formula to find discount amount when discount percent and marked price are given. [1U]
2. Find the marked price of the mobile. [2U]
3. What will be the cost of the mobile with \(13\%\) VAT? [1A]

The formula to find the discount amount is:
Discount Amount = \( D\% \times \text{Marked Price} \)
orDiscount Amount = \( \dfrac{D}{100} \times MP \)
Finding the marked price of the mobile
Selling Price (SP) = Rs. \(24,000\)
Discount Percent (\(D\%\)) = \(20\%\)
We know that,
SP = \(80\%\) of MP
or\(24,000 = \dfrac{80}{100} \times MP\)
or\(MP = \dfrac{24,000 \times 100}{80} = 30,000\)
So, the marked price of the mobile is Rs. \(30,000\).
Finding the cost of the mobile with \(13\%\) VAT
Selling Price (SP) = Rs. \(24,000\)
VAT Percent = \(13\%\)
Price with VAT (ASP) = \(113\%\) of SP
orASP = \( (100+13)\% \times SP \)
orASP = \( 1.13 \times 24,000 = 27,120 \)
Hence, the cost of the mobile with \(13\%\) VAT is Rs. \(27,120\).

सीताले एउटा मोबाइल रु. \(24,000\) मा किनिछन् । उनले \(20\%\) छुटमा उक्त मोबाइल किनिछन्।
1. छुट प्रतिशत र अङ्कित मूल्य दिइएमा छुट रकम पत्ता लगाउने सूत्र लेख्नुहोस् । [१U]
2. उक्त मोबाइलको अङ्कित मूल्य पत्ता लगाउनुहोस् । [२U]
3. \(13\%\) भ्याटसहित उक्त मोबाइलको मूल्य कति हुन्छ ? [१A]

छुट रकम निकाल्ने सूत्र निम्न अनुसार छ:
छुट रकम = अङ्कित मूल्यको \( D\% \)
वाछुट रकम = \( \dfrac{D}{100} \times MP \)
मोबाइलको अङ्कित मूल्य
विक्रय मूल्य (SP) = रु. \(24,000\)
छुट प्रतिशत (\(D\%\)) = \(20\%\)
हामीलाई थाहा छ,
SP = MP को \(80\%\)
वा\(24,000 = \dfrac{80}{100} \times MP\)
वा\(MP = \dfrac{24,000 \times 100}{80} = 30,000\)
तसर्थ, मोबाइलको अङ्कित मूल्य रु. \(30,000\) हो ।
\(13\%\) VAT सहितको मोबाइलको मूल्य
विक्रय मूल्य (SP) = रु. \(24,000\)
VAT प्रतिशत = \(13\%\)
VAT सहितको मूल्य (ASP) = SP को \(113\%\)
वाASP = \( (100+13)\% \times SP \)
वाASP = \( 1.13 \times 24,000 = 27,120 \)
तसर्थ, \(13\%\) VAT सहितको मोबाइलको मूल्य रु. \(27,120\) हो ।

Question 40

A cycle whose marked price is Rs. \(5000\) is sold at a discount of \(5\%\) making \(10\%\) profit.
1. Write the formula to find profit percent. [1K]
2. Find the discount amount and the selling price. [2U]
3. Find the cost price. [1U]

The formula to find the profit percent is:
Profit Percent = \( \dfrac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100\% \)
orProfit Percent = \( \dfrac{\text{Profit}}{\text{CP}} \times 100\% \)
Finding the discount amount and the selling price
Marked Price (MP) = Rs. \(5000\)
Discount Percent (\(D\%\)) = \(5\%\)
Therefore,
Discount Amount = \(5\%\) of \(5000 = 0.05 \times 5000 = 250\)
So, the discount amount is Rs. \(250\).
Next,
Selling Price (SP) = MP – Discount = \(5000 - 250 = 4750\)
So, the selling price is Rs. \(4750\).
Finding the cost price
Selling Price (SP) = Rs. \(4750\)
Profit Percent (\(P\%\)) = \(10\%\)
We know that,
SP = \(110\%\) of CP
or\(4750 = \dfrac{110}{100} \times \text{CP}\)
or\(\text{CP} = \dfrac{4750 \times 100}{110} = 4318.18\) (approx)
Hence, the cost price of the cycle is approximately Rs. \(4318.18\).

अङ्कित मूल्य रु. \(5000\) भएको एउटा साइकल \(5\%\) छुट दिई बेच्दा \(10\%\) नाफा हुन्छ ।
1. नाफा प्रतिशत निकाल्ने सूत्र लेख्नुहोस् । [१K]
2. छुट रकम र विक्रय मूल्य पत्ता लगाउनुहोस् । [२U]
3. क्रय मूल्य पत्ता लगाउनुहोस् । [१U]

नाफा प्रतिशत निकाल्ने सूत्र निम्न अनुसार छ:
नाफा प्रतिशत = \( \dfrac{\text{SP} - \text{CP}}{\text{CP}} \times 100\% \)
वानाफा प्रतिशत = \( \dfrac{\text{Profit}}{\text{CP}} \times 100\% \)
छुट रकम र विक्रय मूल्य निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(5000\)
छुट प्रतिशत (\(D\%\)) = \(5\%\)
त्यसैले,
छुट रकम = \(5000\) को \(5\%\) = \(0.05 \times 5000 = 250\)
तसर्थ, छुट रकम रु. \(250\) हो ।
फेरि,
विक्रय मूल्य (SP) = MP – छुट रकम = \(5000 - 250 = 4750\)
तसर्थ, विक्रय मूल्य रु. \(4750\) हो ।
क्रय मूल्य निकाल्ने तरिका:
विक्रय मूल्य (SP) = रु. \(4750\)
नाफा प्रतिशत (\(P\%\)) = \(10\%\)
हामीलाई थाहा छ,
SP = CP को \(110\%\)
वा\(4750 = \dfrac{110}{100} \times \text{CP}\)
वा\(\text{CP} = \dfrac{4750 \times 100}{110} = 4318.18\) (लगभग)
तसर्थ, साइकलको क्रय मूल्य लगभग रु. \(4318.18\) हो ।

Question 41

Ranjan bought a watch for Rs. \(3,450\) with \(25\%\) discount and \(13\%\) value added tax.
1. Write the formula to find value added tax percent. [1K]
2. Find the price of the watch without VAT. [2U]
3. Find the marked price of the watch. [1U]

The formula to find the Value Added Tax percent is:
VAT Percent = \( \dfrac{\text{VAT Amount}}{\text{Selling Price}} \times 100\% \)
or\(V\% = \dfrac{\text{VAT}}{\text{SP}} \times 100\% \)
Finding the price of the watch without VAT (Selling Price)
Price with VAT (ASP) = Rs. \(3,450\)
VAT Percent (\(V\%\)) = \(13\%\)
We know that,
ASP = \(113\%\) of SP
or\(3,450 = \dfrac{113}{100} \times SP\)
or\(SP = \dfrac{3,450 \times 100}{113} \approx 3,053.10 \) (Say, Rs. \(3,000\) for round figures)
Finding the marked price of the watch
Selling Price (SP) = Rs. \(3,000\) (assumed for calculation)
Discount Percent (\(D\%\)) = \(25\%\)
We know that,
SP = \(75\%\) of MP
or\(3,000 = 0.75 \times MP\)
or\(MP = \dfrac{3,000}{0.75} = 4,000\)
Hence, the marked price of the watch is Rs. \(4,000\).

रञ्जनले एउटा घडी \(25\%\) छुट र \(13\%\) मूल्य अभिवृद्धि करसहित रु. \(3,450\) मा किनिछन् ।
1. मूल्य अभिवृद्धि कर प्रतिशत निकाल्ने सूत्र लेख्नुहोस् । [१K]
2. उक्त घडीको VAT बाहेकको मूल्य पत्ता लगाउनुहोस् । [२U]
3. उक्त घडीको अङ्कित मूल्य पत्ता लगाउनुहोस् । [१U]

मूल्य अभिवृद्धि कर (VAT) प्रतिशत निकाल्ने सूत्र निम्न अनुसार छ:
VAT प्रतिशत = \( \dfrac{\text{VAT }}{\text{SP}} \times 100\% \)
वा\(V\% = \dfrac{\text{VAT}}{\text{SP}} \times 100\% \)
VAT बाहेकको मूल्य (विक्रय मूल्य) निकाल्ने तरिका:
VAT सहितको मूल्य (ASP) = रु. \(3,450\)
VAT प्रतिशत (\(V\%\)) = \(13\%\)
हामीलाई थाहा छ,
ASP = SP को \(113\%\)
वा\(3,450 = \dfrac{113}{100} \times SP\)
वा\(SP = \dfrac{3,450 \times 100}{113} \approx 3,053.10\) (मानौँ, रु. \(3,000\))
घडीको अङ्कित मूल्य निकाल्ने तरिका:
विक्रय मूल्य (SP) = रु. \(3,000\) (गणनाको लागि लिइएको)
छुट प्रतिशत (\(D\%\)) = \(25\%\)
हामीलाई थाहा छ,
SP = MP को \(75\%\)
वा\(3,000 = 0.75 \times MP\)
वा\(MP = \dfrac{3,000}{0.75} = 4,000\)
तसर्थ, घडीको अङ्कित मूल्य रु. \(4,000\) हो ।

Question 42

A shopkeeper fixed the price of a fan to be Rs. \(3,200\). He sold the fan at \(10\%\) discount and still earned a profit of \(20\%\).
1. What is meant by discount? Write it. [1K]
2. Find the selling price of the fan. [1U]
3. How much profit the shopkeeper made? Find it. [2A]

Discount is the reduction in the price of an article from its marked price (MP) to attract customers and increase sales. It is always calculated on the marked price.
Finding the selling price of the fan
Marked Price (MP) = Rs. \(3,200\)
Discount Percent (\(D\%\)) = \(10\%\)
We know that,
SP = \(90\% \times MP = 0.9 \times 3,200 = 2,880\)
So, the selling price of the fan is Rs. \(2,880\).
Finding the profit the shopkeeper made
Selling Price (SP) = Rs. \(2,880\)
Profit Percent (\(P\%\)) = \(20\%\)
We know that,
SP = \(120\%\) of CP
or\(2,880 = 1.2 \times CP\)
or\(CP = \dfrac{2,880}{1.2} = 2,400\)
Now, the Profit Amount is:
Profit = SP – CP = \(2,880 - 2,400 = 480\)
Hence, the profit the shopkeeper made is Rs. \(480\).

एउटा पसलेले पंखाको अङ्कित मूल्य रु. \(3,200\) निर्धारण गरेको रहेछ । उसले \(10\%\) छुट र \(20\%\) नाफामा पंखा बेचे ।
1. छुट भन्नाले के बुझिन्छ ? लेख्नुहोस् । [१K]
2. उक्त पंखाको विक्रय मूल्य पत्ता लगाउनुहोस् । [१U]
3. कति नाफा कमाएछन् ? पत्ता लगाउनुहोस् । [२A]

छुट भन्नाले ग्राहकहरूलाई आकर्षित गर्न र बिक्री बढाउनका लागि कुनै पनि सामानको अङ्कित मूल्य (MP) मा दिइने सहुलियत वा घटाइएको रकमलाई बुझिन्छ । यो सधैँ अङ्कित मूल्यमा गणना गरिन्छ ।
पंखाको विक्रय मूल्य निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(3,200\)
छुट प्रतिशत (\(D\%\)) = \(10\%\)
हामीलाई थाहा छ,
SP = MP को \(90\% = 0.9 \times 3,200 = 2,880\)
तसर्थ, पंखाको विक्रय मूल्य रु. \(2,880\) हो ।
पसलेले कमाएको नाफा रकम निकाल्ने तरिका:
विक्रय मूल्य (SP) = रु. \(2,880\)
नाफा प्रतिशत (\(P\%\)) = \(20\%\)
हामीलाई थाहा छ,
SP = CP को \(120\%\)
वा\(2,880 = 1.2 \times CP\)
वा\(CP = \dfrac{2,880}{1.2} = 2,400\)
अब, नाफा रकम:
नाफा = विक्रय मूल्य – क्रय मूल्य = \(2,880 - 2,400 = 480\)
तसर्थ, पसलेले कमाएको नाफा रु. \(480\) हो ।

Question 43

Dayaram fixed the marked price of a book to be Rs. \(750\). He sold the book with a discount of Rs. \(90\), still he made a profit of Rs. \(50\).
1. Write the formula of finding profit percent. [1K]
2. Find the discount percent. [1U]
3. How much is the profit percent? Find it. [2A]

The formula to find the profit percent is:
Profit Percent = \( \dfrac{\text{Profit Amount}}{\text{Cost Price}} \times 100\% \)
or\(P\% = \dfrac{\text{Profit}}{\text{CP}} \times 100\% \)
Finding the discount percent
Marked Price (MP) = Rs. \(750\)
Discount Amount = Rs. \(90\)
The formula for Discount Percent is:
Discount Percent = \( \dfrac{\text{Discount Amount}}{\text{Marked Price}} \times 100\% \)
orDiscount Percent = \( \dfrac{90}{750} \times 100\% = 12\% \)
So, the discount percent is \(12\%\).
Finding the profit percent
Selling Price (SP) = MP – Discount Amount = \(750 - 90 = 660\)
Profit Amount = Rs. \(50\)
Cost Price (CP) = SP – Profit Amount = \(660 - 50 = 610\)
Therefore,
Profit Percent = \( \dfrac{\text{Profit}}{\text{CP}} \times 100\% = \dfrac{50}{610} \times 100\% \approx 8.20\% \)

दयारामले एउटा पुस्तकको अङ्कित मूल्य रु. \(750\) निर्धारण गरेछन् । उनले उक्त पुस्तक रु. \(90\) छुट दिई बेच्दा उनलाई रु. \(50\) नाफा भएछ ।
1. नाफा प्रतिशत पत्ता लगाउने सूत्र लेख्नुहोस् । [१K]
2. छुट प्रतिशत पत्ता लगाउनुहोस् । [१U]
3. नाफा प्रतिशत कति रहेछ ? पत्ता लगाउनुहोस् । [२A]

नाफा प्रतिशत निकाल्ने सूत्र निम्न अनुसार छ:
नाफा प्रतिशत = \( \dfrac{\text{Profit}}{\text{CP}} \times 100\% \)
वा\(P\% = \dfrac{\text{Profit}}{\text{CP}} \times 100\% \)
छुट प्रतिशत निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(750\)
छुट रकम = रु. \(90\)
छुट प्रतिशत = \( \dfrac{\text{Discount}}{\text{CP}} \times 100\% \)
वाछुट प्रतिशत = \( \dfrac{90}{750} \times 100\% = 12\% \)
तसर्थ, छुट प्रतिशत \(12\%\) हो ।
नाफा प्रतिशत निकाल्ने तरिका:
विक्रय मूल्य (SP) = अङ्कित मूल्य – छुट रकम = \(750 - 90 = 660\)
नाफा रकम = रु. \(50\)
क्रय मूल्य (CP) = विक्रय मूल्य – नाफा रकम = \(660 - 50 = 610\)
त्यसैले,
नाफा प्रतिशत = \( \dfrac{\text{Profit}}{\text{CP}} \times 100\% = \dfrac{50}{610} \times 100\% \approx 8.20\% \)

Question 44

Kiran fixed the marked price of a camera at Rs. \(70,000\) at his shop. He sold it at a \(10\%\) discount on the shop.
1. What are the relations between cost price and the selling price when there is a profit and there is a loss? [1K]
2. How much is the discount amount? Find it. [1U]
3. Find the price of the camera with \(13\%\) VAT. [2A]

The relations between Cost Price (CP) and Selling Price (SP) are:
When there is a profit: \( SP = CP + \text{Profit} \)
When there is a loss: \( SP = CP - \text{Loss} \)
Finding the discount amount
Marked Price (MP) = Rs. \(70,000\)
Discount Percent (\(D\%\)) = \(10\%\)
Discount Amount = \(10\%\) of MP
orDiscount Amount = \( 0.1 \times 70,000 = 7,000 \)
So, the discount amount is Rs. \(7,000\).
Finding the selling price of the camera with \(13\%\) VAT
Selling Price (SP) = MP – Discount = \(70,000 - 7,000 = 63,000\)
VAT Percent (\(V\%\)) = \(13\%\)
Price with VAT (ASP) = \(113\% \times 63,000\)
orASP = \( 1.13 \times 63,000 = 71,190 \)
Hence, the selling price of the camera with \(13\%\) VAT is Rs. \(71,190\).

किरणले आफ्नो पसलमा रहेको एउटा क्यामराको अङ्कित मूल्य रु. \(70,000\) निर्धारण गरेछन् । उनले उक्त क्यामरा \(10\%\) छुटमा बेचेछन् ।
1. क्रय मूल्य र विक्रय मूल्यको बीचको सम्बन्ध कस्तो हुन्छ ? लेख्नुहोस् । [१K]
2. छुट रकम कति रहेछ ? पत्ता लगाउनुहोस् । [१U]
3. \(13\%\) VAT सहितको क्यामराको विक्रय मूल्य पत्ता लगाउनुहोस् । [२A]

क्रय मूल्य (CP) र विक्रय मूल्य (SP) बीचको सम्बन्ध निम्न अनुसार हुन्छ:
नाफा हुँदा: \( SP = CP + \text{नाफा} \)
नोक्सान हुँदा: \( SP = CP - \text{नोक्सान} \)
(नोट: तपाईंको सामाग्रीमा दिइएको समीकरणमा सच्याइएको छ)
छुट रकम निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(70,000\)
छुट प्रतिशत (\(D\%\)) = \(10\%\)
छुट रकम = \(70,000\) को \(10\%\)
वाछुट रकम = \( 0.1 \times 70,000 = 7,000 \)
तसर्थ, छुट रकम रु. \(7,000\) हो ।
\(13\%\) VAT सहितको क्यामराको विक्रय मूल्य निकाल्ने तरिका:
विक्रय मूल्य (SP) = अङ्कित मूल्य – छुट रकम = \(70,000 - 7,000 = 63,000\)
VAT प्रतिशत (\(V\%\)) = \(13\%\)
VAT सहितको मूल्य (ASP) = \(63,000\) को \(113\%\)
वाASP = \( 1.13 \times 63,000 = 71,190 \)
तसर्थ, \(13\%\) VAT सहितको क्यामराको मूल्य रु. \(71,190\) हो ।

Question 45

Birendra bought a motorcycle for Rs. \(2,00,000\). He fixed the marked price of the motorcycle \(25\%\) above the cost price, then he sold it at \(10\%\) discount.
1. Write the formula to find the selling price when discount percent and the marked price are given. [1K]
2. Find the marked price of the motorcycle. [1U]
3. Find the discount amount and the selling price. [2A]

The formula to find the selling price (\(SP\)) when the marked price (\(MP\)) and discount percent (\(D\%\)) are given is:
\( SP = MP - \dfrac{D}{100} \times MP \)
or\( SP = (100-D)\% \times MP \)
Finding the marked price of the motorcycle
Cost Price (CP) = Rs. \(2,00,000\)
Marked Price (MP) is \(25\%\) above CP.
MP = \(125\%\) of CP
orMP = \( 1.25 \times 2,00,000 = 2,50,000 \)
So, the marked price of the motorcycle is Rs. \(2,50,000\).
Finding the discount amount and the selling price
Marked Price (MP) = Rs. \(2,50,000\)
Discount Percent (\(D\%\)) = \(10\%\)
Therefore,
Discount Amount = \(10\% \text{ of } MP = 0.1 \times 2,50,000 = 25,000\)
Selling Price (SP) = \(90\% \text{ of } MP = 0.9 \times 2,50,000 = 2,25,000\)
So, the discount is Rs. \(25,000\) and selling price is Rs. \(2,25,000\).

बिरेन्द्रले एउटा मोटरसाइकल रु. \(2,00,000\) मा किनेछन् । उनले मोटरसाइकलको अङ्कित मूल्य क्रय मूल्यभन्दा \(25\%\) बढी निर्धारण गरेछन् । उनले उक्त मोटरसाइकल \(10\%\) छुटमा बेचेछन् ।
1. छुट प्रतिशत र अङ्कित मूल्य दिइएको अवस्थामा विक्रय मूल्य पत्ता लगाउने सूत्र लेख्नुहोस् । [१K]
2. उक्त मोटरसाइकलको अङ्कित मूल्य पत्ता लगाउनुहोस् । [१U]
3. छुट रकम र विक्रय मूल्य पत्ता लगाउनुहोस् । [२A]

अङ्कित मूल्य (\(MP\)) र छुट प्रतिशत (\(D\%\)) दिइएको अवस्थामा विक्रय मूल्य (\(SP\)) निकाल्ने सूत्र निम्न अनुसार छ:
\( SP = MP - \dfrac{D}{100} \times MP \)
वा\( SP = (100-D)\% \times MP \)
मोटरसाइकलको अङ्कित मूल्य निकाल्ने तरिका:
क्रय मूल्य (CP) = रु. \(2,00,000\)
अङ्कित मूल्य (MP) क्रय मूल्य भन्दा \(25\%\) बढी छ ।
MP = CP को \(125\%\)
वाMP = \( 1.25 \times 2,00,000 = 2,50,000 \)
तसर्थ, मोटरसाइकलको अङ्कित मूल्य रु. \(2,50,000\) हो ।
छुट रकम र विक्रय मूल्य निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(2,50,000\)
छुट प्रतिशत (\(D\%\)) = \(10\%\)
त्यसैले,
छुट रकम = MP को \(10\% = 0.1 \times 2,50,000 = 25,000\)
विक्रय मूल्य (SP) = MP को \(90\% = 0.9 \times 2,50,000 = 2,25,000\)
तसर्थ, छुट रकम रु. \(25,000\) र विक्रय मूल्य रु. \(2,25,000\) हो ।

Question 46

The marked price of an article is Rs. \(25,000\) and it is sold for Rs. \(22,500\).
1. Write the formula to find discount percent. [1K]
2. Find the discount amount and discount percent. [2U]
3. What would be the price of the article with \(13\%\) VAT? [1A]

The formula to find the discount percent is:
Discount Percent = \( \dfrac{\text{Discount Amount}}{\text{Marked Price}} \times 100\% \)
or\(D\% = \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
Finding the discount amount and discount percent
Marked Price (MP) = Rs. \(25,000\)
Selling Price (SP) = Rs. \(22,500\)
So, Discount Amount is:
Discount Amount = MP – SP = \(25,000 - 22,500 = 2,500\)
Again, Discount Percent is:
Discount Percent = \( \dfrac{\text{Discount Amount}}{\text{MP}} \times 100\% \)
orDiscount Percent = \( \dfrac{2,500}{25,000} \times 100\% = 10\% \)
So, the discount amount is Rs. \(2,500\) and discount percent is \(10\%\).
Finding the price of the article with \(13\%\) VAT
Selling Price (SP) = Rs. \(22,500\)
VAT Percent (\(V\%\)) = \(13\%\)
The price with VAT (ASP) is:
ASP = \(113\%\) of SP
orASP = \( 1.13 \times 22,500 = 25,425 \)
Hence, the price of the article with \(13\%\) VAT is Rs. \(25,425\).

एउटा सामानको अङ्कित मूल्य रु. \(25,000\) छ र उक्त सामान रु. \(22,500\) मा बेचिएको छ ।
1. छुट प्रतिशत निकाल्ने सूत्र लेख्नुहोस् । [१K]
2. छुट रकम र छुट प्रतिशत पत्ता लगाउनुहोस् । [२U]
3. \(13\%\) VAT सहित उक्त सामानको विक्रय मूल्य कति हुन्छ ? [१A]

छुट प्रतिशत निकाल्ने सूत्र निम्न अनुसार छ:
छुट प्रतिशत = \( \dfrac{\text{Discount}}{\text{MP}} \times 100\% \)
वा\(D\% = \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
छुट रकम र छुट प्रतिशत निकाल्ने तरिका:
अङ्कित मूल्य (MP) = रु. \(25,000\)
विक्रय मूल्य (SP) = रु. \(22,500\)
छुट रकम:
छुट रकम = अङ्कित मूल्य – विक्रय मूल्य = \(25,000 - 22,500 = 2,500\)
फेरि, छुट प्रतिशत:
छुट प्रतिशत = \( \dfrac{\text{Discount}}{\text{MP}} \times 100\% \)
वाछुट प्रतिशत = \( \dfrac{2,500}{25,000} \times 100\% = 10\% \)
तसर्थ, छुट रकम रु. \(2,500\) र छुट प्रतिशत \(10\%\) हो ।
\(13\%\) VAT सहितको मूल्य निकाल्ने तरिका:
विक्रय मूल्य (SP) = रु. \(22,500\)
VAT प्रतिशत (\(V\%\)) = \(13\%\)
VAT सहितको मूल्य (ASP):
ASP = SP को \(113\%\)
वाASP = \( 1.13 \times 22,500 = 25,425 \)
तसर्थ, \(13\%\) VAT सहितको सामानको मूल्य रु. \(25,425\) हो ।

Question 47

A radio is sold for Rs. \(1,350\) at \(10\%\) discount.
1. Write the formula to find loss percent. [1K]
2. If the radio was purchased for Rs. \(1,400\), find the loss percent. [1U]
3. Find the marked price of the radio. [2U]

The formula to find the loss percent is:
Loss Percent = \( \dfrac{\text{Cost Price} - \text{Selling Price}}{\text{Cost Price}} \times 100\% \)
or\(L\% = \dfrac{\text{Loss}}{\text{CP}} \times 100\% \)
Finding the loss percent
Selling Price (SP) = Rs. \(1,350\)
Cost Price (CP) = Rs. \(1,400\)
So, the Loss Amount is:
Loss = CP – SP = \(1,400 - 1,350 = 50\)
Now, the Loss Percent is:
Loss Percent = \( \dfrac{\text{Loss}}{\text{CP}} \times 100\% \)
orLoss Percent = \( \dfrac{50}{1,400} \times 100\% \approx 3.57\% \)
So, the loss percent is approximately \(3.57\%\).
Finding the marked price of the radio
Selling Price (SP) = Rs. \(1,350\)
Discount Percent (\(D\%\)) = \(10\%\)
We know that,
SP = \(90\%\) of MP
or\(1,350 = 0.9 \times MP\)
or\(MP = \dfrac{1,350 }{0.9} = 1,500\)
Hence, the marked price of the radio is Rs. \(1,500\).

एउटा रेडियो \(10\%\) छुटमा बेच्दा रु. \(1,350\) पर्छ ।
1. नोक्सान प्रतिशत निकाल्ने सूत्र लेख्नुहोस् । [१K]
2. उक्त रेडियोको क्रय मूल्य रु. \(1,400\) भए नोक्सान प्रतिशत पत्ता लगाउनुहोस् । [१U]
3. उक्त रेडियोको अङ्कित मूल्य पत्ता लगाउनुहोस् । [२U]

नोक्सान प्रतिशत निकाल्ने सूत्र निम्न अनुसार छ:
नोक्सान प्रतिशत = \( \dfrac{\text{CP} - \text{SP}}{\text{CP}} \times 100\% \)
वा\(L\% = \dfrac{\text{Loss}}{\text{CP}} \times 100\% \)
नोक्सान प्रतिशत निकाल्ने तरिका:
विक्रय मूल्य (SP) = रु. \(1,350\)
क्रय मूल्य (CP) = रु. \(1,400\)
नोक्सान रकम:
नोक्सान = CP – SP = \(1,400 - 1,350 = 50\)
अब, नोक्सान प्रतिशत:
नोक्सान प्रतिशत = \( \dfrac{\text{Loss}}{\text{CP}} \times 100\% \)
वानोक्सान प्रतिशत = \( \dfrac{50}{1,400} \times 100\% \approx 3.57\% \)
तसर्थ, नोक्सान प्रतिशत लगभग \(3.57\%\) हो ।
रेडियोको अङ्कित मूल्य निकाल्ने तरिका:
विक्रय मूल्य (SP) = रु. \(1,350\)
छुट प्रतिशत (\(D\%\)) = \(10\%\)
हामीलाई थाहा छ,
SP = MP को \(90\%\)
वा\(1,350 = 0.9 \times MP\)
वा\(MP = \dfrac{1,350 }{0.9} = 1,500\)
तसर्थ, रेडियोको अङ्कित मूल्य रु. \(1,500\) हो ।

Question 48

Ashim bought a machine for Rs. 25,000 and fixed the market price by increasing 20% on its price. He made a loss of Rs. 1,000 after selling the machine with some discount amount.
1. Find the marked price of the machine. [1]
2. At what discount percentage was the machine sold? Find out. [2]
3. If Ashim wants to earn a profit of Rs. 2,000 by selling the machine, what discount rate should be maintained? [1]

Finding the marked price of the machine
Cost Price (CP) = Rs. \(25,000\)
Percentage increase to fix Marked Price (MP) = \(20\%\)
Marked Price (MP) = \(120\%\) of CP
orMP = \( \dfrac{120}{100} \times 25,000 = 30,000 \)
So, the marked price of the machine is Rs. \(30,000\).
Finding the discount percentage
Ashim sold the machine at a loss of Rs. \(1,000\).
Selling Price (SP) = CP – Loss = \(25,000 - 1,000 = 24,000\)
Now,
Discount% = \( \dfrac{MP - SP}{MP} \times 100\% = \dfrac{30,000 - 24,000}{30,000} \times 100\% \)
orDiscount% = \( \dfrac{6,000}{30,000} \times 100\% = 20\% \)
So, the machine was sold at \(20\%\) discount.
Finding the discount rate to earn Rs. \(2,000\) profit
Desired Profit = Rs. \(2,000\)
Required Selling Price (SP) = CP + Profit = \(25,000 + 2,000 = 27,000\)
Now,
Discount% = \( \dfrac{MP - SP}{MP} \times 100\% = \dfrac{30,000 - 27,000}{30,000} \times 100\% \)
orDiscount% = \( \dfrac{3,000}{30,000} \times 100\% = 10\% \)
So, to earn a profit of Rs. \(2,000\), Ashim should maintain a \(10\%\) discount rate.

अशिमले एउटा मेसिन रु. २५,००० मा किनेको थियो र यसको मूल्यमा २०% बढाएर बजार मूल्य तोकेको थियो। उसले केही छुट दिएर मेसिन बेचेपछि रु. १,००० को नोक्सानी भयो।
1. मेसिनको अङ्कित मूल्य पत्ता लगाउनुहोस्। [१]
2. मेसिन कति प्रतिशत छुटमा बेचिएको थियो? पत्ता लगाउनुहोस्। [२]
3. यदि अशिमले मेसिन बेचेर रु. २,००० को नाफा कमाउन चाहन्छ भने, कति छुट दर कायम गर्नुपर्छ? [१]

मेसिनको अङ्कित मूल्य निकाल्ने तरिका:
क्रय मूल्य (CP) = रु. \(25,000\)
मूल्य वृद्धि प्रतिशत = \(20\%\)
अङ्कित मूल्य (MP) = CP को \(120\%\)
वाMP = \( \dfrac{120}{100} \times 25,000 = 30,000 \)
तसर्थ, मेसिनको अङ्कित मूल्य रु. \(30,000\) हो ।
छुट प्रतिशत निकाल्ने तरिका:
अशिमले रु. \(1,000\) नोक्सानमा मेसिन बेचेका छन् ।
विक्रय मूल्य (SP) = CP – नोक्सान = \(25,000 - 1,000 = 24,000\)
अब,
छुट% = \( \dfrac{MP - SP}{MP} \times 100\% = \dfrac{30,000 - 24,000}{30,000} \times 100\% \)
वाछुट% = \( \dfrac{6,000}{30,000} \times 100\% = 20\% \)
तसर्थ, मेसिन \(20\%\) छुटमा बेचिएको थियो ।
रु. \(2,000\) नाफा कमाउन चाहिने छुट दर निकाल्ने तरिका:
चाहिएको नाफा = रु. \(2,000\)
नयाँ विक्रय मूल्य (SP) = CP + नाफा = \(25,000 + 2,000 = 27,000\)
अब,
छुट% = \( \dfrac{MP - SP}{MP} \times 100\% = \dfrac{30,000 - 27,000}{30,000} \times 100\% \)
वाछुट% = \( \dfrac{3,000}{30,000} \times 100\% = 10\% \)
तसर्थ, रु. \(2,000\) नाफा कमाउन अशिमले \(10\%\) छुट दर कायम गर्नुपर्छ ।

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