G8_Simple Interest_BLE_Questions

Question 1

• A man deposited Rs 60,000 in a bank. If he received Rs 16,200 as interest from the bank after 3 years,
  1. Find the total amount he received from the bank.[1]
  2. Find the rate of interest.[2]
  3. If he divided the received interest between two daughters Rusmita and Susmita in the ratio 2:3, then how much money did Rusmita and Susmita get?[2]
1. Total amount received:
   Principal (P) = Rs. 60,000
   Interest (I) = Rs. 16,200
   Thus,
   Amount (A) = P + I = 60,000 + 16,200 = 76,200
   So, the total amount received is Rs. 76,200.
2. Rate of interest:
   Principal (P) = Rs. 60,000
   Time (T) = 3 years
   Interest (I) = Rs. 16,200
   We know,
   Rate (R) = \( \dfrac{I \times 100}{P \times T} = \dfrac{16,200 \times 100}{60,000 \times 3} = 9\% \)
   So, the rate of interest is 9% per annum.
3. Money received by daughters:
   Total Interest = Rs. 16,200
   Ratio = 2:3 (Rusmita : Susmita)
   Sum of ratio = 2 + 3 = 5
   Thus,
   Rusmita's share = \( \dfrac{2}{5} \times 16,200 = 6,480 \)
   Susmita's share = \( \dfrac{3}{5} \times 16,200 = 9,720 \)
   So, Rusmita got Rs. 6,480 and Susmita got Rs. 9,720.
• एकजना मानिसले बैंकमा रु. 60,000 जम्मा गरे । यदि उनले 3 वर्षपछि बैंकबाट रु. 16,200 ब्याज प्राप्त गरे भने:
  1. उनले बैंकबाट प्राप्त गरेको जम्मा मिश्रधन (Amount) पत्ता लगाउनुहोस् । [1]
  2. ब्याजको दर पत्ता लगाउनुहोस् । [2]
  3. यदि उनले प्राप्त गरेको ब्याजलाई आफ्ना दुई छोरीहरू रुस्मिता र सुस्मिताका बीच 2:3 को अनुपातमा बाँडे भने, रुस्मिता र सुस्मिताले कति-कति रकम पाए ? [2]
1. बैंकबाट प्राप्त जम्मा मिश्रधन:
   साँवा (P) = रु. 60,000
   ब्याज (I) = रु. 16,200
   यसरी,
   मिश्रधन (A) = P + I = 60,000 + 16,200 = 76,200
   तसर्थ, उनले प्राप्त गरेको जम्मा रकम रु. 76,200 हो ।
2. ब्याजको दर:
   साँवा (P) = रु. 60,000
   समय (T) = 3 वर्ष
   ब्याज (I) = रु. 16,200
   हामीलाई थाहा छ,
   दर (R) = \( \dfrac{I \times 100}{P \times T} = \dfrac{16,200 \times 100}{60,000 \times 3} = 9\% \)
   तसर्थ, ब्याजको दर 9% प्रति वर्ष हो ।
3. छोरीहरूले पाएको रकम:
   जम्मा बाँडिने ब्याज = रु. 16,200
   अनुपात = 2:3 (रुस्मिता : सुस्मिता)
   अनुपातको योग = 2 + 3 = 5
   यसरी,
   रुस्मिताले पाएको रकम = \( \dfrac{2}{5} \times 16,200 = 6,480 \)
   सुस्मिताले पाएको रकम = \( \dfrac{3}{5} \times 16,200 = 9,720 \)
   तसर्थ, रुस्मिताले रु. 6,480 र सुस्मिताले रु. 9,720 पाए ।

Question 2

• Elisza took a loan of Rs 80,000 from Nabil Bank for 4 years at the rate of 10% p.a. simple interest.
  1. Write amount (A) in terms of principal (P) and interest (I).[1]
  2. How much interest should she pay in 4 years? Calculate it.[2]
  3. Find the amount.[1]
1. Amount (A) in terms of P and I:
   Amount (A) = Principal (P) + Interest (I)
2. Interest for 4 years:
   Principal (P) = Rs. 80,000
   Time (T) = 4 years
   Rate (R) = 10%
   We know,
   Interest (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{80,000 \times 4 \times 10}{100} = 32,000 \)
   So, she should pay Rs. 32,000 as interest.
3. Find the amount:
   Principal (P) = Rs. 80,000
   Interest (I) = Rs. 32,000
   Thus,
   Amount (A) = P + I = 80,000 + 32,000 = 1,12,000
   So, the amount is Rs. 1,12,000.
• एलिसाले नबिल बैंकबाट वार्षिक 10% साधारण ब्याजदरमा 4 वर्षका लागि रु. 80,000 ऋण लिइन् भने:
  1. मिश्रधन (A) लाई साँवा (P) र ब्याज (I) को रूपमा लेख्नुहोस् । [1]
  2. उनले 4 वर्षमा कति ब्याज तिर्नुपर्छ ? गणना गर्नुहोस् । [2]
  3. मिश्रधन पत्ता लगाउनुहोस् । [1]
1. मिश्रधन (A) को सूत्र:
   मिश्रधन (A) = साँवा (P) + ब्याज (I)
2. 4 वर्षको ब्याज:
   साँवा (P) = रु. 80,000
   समय (T) = 4 वर्ष
   दर (R) = 10%
   हामीलाई थाहा छ,
   ब्याज (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{80,000 \times 4 \times 10}{100} = 32,000 \)
   तसर्थ, उनले 4 वर्षमा रु. 32,000 ब्याज तिर्नुपर्छ ।
3. मिश्रधन:
   साँवा (P) = रु. 80,000
   ब्याज (I) = रु. 32,000
   यसरी,
   मिश्रधन (A) = P + I = 80,000 + 32,000 = 1,12,000
   तसर्थ, मिश्रधन रु. 1,12,000 हो ।

Question 3

• Bhargab deposited Rs 50,000 in a bank. After 2 years, he received simple interest of Rs 10,000.
  1. What is the amount after 2 years? Find it.[1]
  2. Find the rate of interest per annum.[2]
  3. If Bhargab had deposited the same amount for only 1 year, how much less interest would he have received?[1]
1. Amount after 2 years:
   Principal (P) = Rs. 50,000
   Interest (I) = Rs. 10,000
   Thus,
   Amount (A) = P + I = 50,000 + 10,000 = 60,000
   So, the amount after 2 years is Rs. 60,000.
2. Rate of interest per annum:
   Principal (P) = Rs. 50,000
   Time (T) = 2 years
   Interest (I) = Rs. 10,000
   We know,
   Rate (R) = \( \dfrac{I \times 100}{P \times T} = \dfrac{10,000 \times 100}{50,000 \times 2} = 10\% \)
   So, the rate of interest is 10% per annum.
3. Difference in interest:
   Interest for 2 years = Rs. 10,000
   Interest for 1 year = \( \dfrac{50,000 \times 1 \times 10}{100} = 5,000 \)
   Thus,
   Less interest = 10,000 - 5,000 = 5,000
   So, he would have received Rs. 5,000 less interest.
• भार्गवले एउटा बैंकमा रु. 50,000 जम्मा गरे । 2 वर्षपछि उनले रु. 10,000 साधारण ब्याज प्राप्त गरे भने:
  1. 2 वर्षपछिको मिश्रधन (Amount) कति हुन्छ ? पत्ता लगाउनुहोस् । [1]
  2. ब्याजको वार्षिक दर पत्ता लगाउनुहोस् । [2]
  3. यदि भार्गवले सोही रकम 1 वर्षको लागि मात्र जम्मा गरेको भए, उनले कति कम ब्याज पाउँथे होलान् ? [1]
1. 2 वर्षपछिको मिश्रधन:
   साँवा (P) = रु. 50,000
   ब्याज (I) = रु. 10,000
   यसरी,
   मिश्रधन (A) = P + I = 50,000 + 10,000 = 60,000
   तसर्थ, 2 वर्षपछिको मिश्रधन रु. 60,000 हुन्छ ।
2. ब्याजको वार्षिक दर:
   साँवा (P) = रु. 50,000
   समय (T) = 2 वर्ष
   ब्याज (I) = रु. 10,000
   हामीलाई थाहा छ,
   दर (R) = \( \dfrac{I \times 100}{P \times T} = \dfrac{10,000 \times 100}{50,000 \times 2} = \dfrac{1,000,000}{100,000} = 10\% \)
   तसर्थ, ब्याजको दर 10% प्रति वर्ष हो ।
3. ब्याजको फरक:
   2 वर्षको ब्याज = रु. 10,000
   1 वर्षको ब्याज = \( \dfrac{50,000 \times 1 \times 10}{100} = 5,000 \)
   यसरी,
   कम ब्याज रकम = 10,000 - 5,000 = 5,000
   तसर्थ, उनले रु. 5,000 कम ब्याज पाउने थिए ।

Question 4

• Anita deposited Rs 3,50,000 in a bank at the rate of 12% per annum for 2 years.
  1. Write the formula to calculate the amount.[1]
  2. How much interest does Anita get in 2 years?[2]
  3. 18 men can complete a work in 30 days. How many men can finish the same work in 36 days?[2]
1. Formula to calculate amount:
   Amount (A) = Principal (P) + Interest (I)
   or,
   Amount (A) = \( P \left( 1 + \dfrac{T \times R}{100} \right) \)
2. Interest for 2 years:
   Principal (P) = Rs. 3,50,000
   Time (T) = 2 years
   Rate (R) = 12%
   Thus,
   Interest (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{3,50,000 \times 2 \times 12}{100} = 84,000 \)
   So, Anita gets Rs. 84,000 interest.
3. Work and Men calculation:
   To finish work in 30 days, men required = 18
   To finish work in 1 day, men required = \( 18 \times 30 \)
   Thus,
   To finish work in 36 days, men required = \( \dfrac{18 \times 30}{36} = 15 \)
   So, 15 men can finish the work in 36 days.
• अनिताले वार्षिक 12% ब्याजदरमा 2 वर्षका लागि एउटा बैंकमा रु. 3,50,000 जम्मा गरिन् भने:
  1. मिश्रधन (Amount) गणना गर्ने सूत्र लेख्नुहोस् । [1]
  2. अनिताले 2 वर्षमा कति ब्याज प्राप्त गर्छिन् ? [2]
  3. 18 जना मानिसले एउटा काम 30 दिनमा पूरा गर्न सक्छन् भने, कति जना मानिसले सोही काम 36 दिनमा सिध्याउन सक्छन् ? [2]
1. मिश्रधन गणना गर्ने सूत्र:
   मिश्रधन (A) = P + I
   वा
   मिश्रधन (A) = \( P \left( 1 + \dfrac{T \times R}{100} \right) \)
2. 2 वर्षको ब्याज:
   साँवा (P) = रु. 3,50,000
   समय (T) = 2 वर्ष
   दर (R) = 12%
   यसरी,
   ब्याज (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{3,50,000 \times 2 \times 12}{100} = 84,000 \)
   तसर्थ, अनिताले रु. 84,000 ब्याज पाउँछिन् ।
3. काम र मानिसको संख्या:
   30 दिनमा काम सिध्याउन चाहिने मानिस = 18 जना
   1 दिनमा काम सिध्याउन चाहिने मानिस = \( 18 \times 30 \) जना
   यसरी,
   36 दिनमा काम सिध्याउन चाहिने मानिस = \( \dfrac{18 \times 30}{36} = \dfrac{540}{36} = 15 \) जना
   तसर्थ, सो काम 36 दिनमा सिध्याउन 15 जना मानिस चाहिन्छन् ।

Question 5

• Anu had borrowed a loan of Rs 6,000 from a bank 4 years ago. She paid a total amount of Rs 9,000 and cleared the loan.
  1. Find the simple interest.[2]
  2. What was the rate of interest?[2]
  3. In how many years will the principal and interest be equal?[1]
1. Simple Interest:
   Principal (P) = Rs. 6,000
   Amount (A) = Rs. 9,000
   Thus,
   Interest (I) = A - P = 9,000 - 6,000 = 3,000
   So, the simple interest is Rs. 3,000.
2. Rate of interest:
   Principal (P) = Rs. 6,000
   Time (T) = 4 years
   Interest (I) = Rs. 3,000
   We know,
   Rate (R) = \( \dfrac{I \times 100}{P \times T} = \dfrac{3,000 \times 100}{6,000 \times 4} = 12.5\% \)
   So, the rate of interest was 12.5% per annum.
3. Time for principal and interest to be equal:
   Here, Interest (I) = Principal (P).
   We know, \( T = \dfrac{I \times 100}{P \times R} \)
   Since I = P, the formula becomes \( T = \dfrac{100}{R} \).
   Thus,
   Time (T) = \( \dfrac{100}{12.5} = 8 \) years
   So, the principal and interest will be equal in 8 years.
• अनुले 4 वर्षअघि एउटा बैंकबाट रु. 6,000 ऋण लिएकी थिइन् । उनले जम्मा रु. 9,000 तिरेर उक्त ऋण चुक्ता गरिन् भने:
  1. साधारण ब्याज पत्ता लगाउनुहोस् । [2]
  2. ब्याजको दर कति थियो ? [2]
  3. कति वर्षमा साँवा र ब्याज बराबर हुन्छन् ? [1]
1. साधारण ब्याज:
   साँवा (P) = रु. 6,000
   मिश्रधन (A) = रु. 9,000
   यसरी,
   ब्याज (I) = A - P = 9,000 - 6,000 = 3,000
   तसर्थ, साधारण ब्याज रु. 3,000 हो ।
2. ब्याजको दर:
   साँवा (P) = रु. 6,000
   समय (T) = 4 वर्ष
   ब्याज (I) = रु. 3,000
   हामीलाई थाहा छ,
   दर (R) = \( \dfrac{I \times 100}{P \times T} = \dfrac{3,000 \times 100}{6,000 \times 4} = \dfrac{300,000}{24,000} = 12.5\% \)
   तसर्थ, ब्याजको दर 12.5% प्रति वर्ष थियो ।
3. साँवा र ब्याज बराबर हुने समय:
   यहाँ, ब्याज (I) = साँवा (P) हुनुपर्छ ।
   हामीलाई थाहा छ, \( T = \dfrac{I \times 100}{P \times R} \)
   जब I = P हुन्छ, \( T = \dfrac{100}{R} \)
   यसरी,
   समय (T) = \( \dfrac{100}{12.5} = 8 \) वर्ष
   तसर्थ, 8 वर्षमा साँवा र ब्याज बराबर हुन्छन् ।

Question 6

• Ruby took a loan for 2 years at the simple interest rate of 10% per annum. If the interest for that period was Rs 2,000,
  1. Define interest.[1]
  2. How much loan did she take? Find it.[2]
  3. Find the ratio between interest and principal.[1]
1. Definition of Interest:
   Interest is the extra money paid by a borrower to a lender or bank for the use of the borrowed principal amount.
2. Loan amount (Principal):
   Time (T) = 2 years
   Rate (R) = 10%
   Interest (I) = Rs. 2,000
   We know,
   Principal (P) = \( \dfrac{I \times 100}{T \times R} = \dfrac{2,000 \times 100}{2 \times 10} = 10,000 \)
   So, she took a loan of Rs. 10,000.
3. Ratio between Interest and Principal:
   Interest = Rs. 2,000
   Principal = Rs. 10,000
   Thus,
   Ratio = \( \dfrac{2,000}{10,000} = \dfrac{1}{5} \)
   So, the ratio between interest and principal is 1:5.
• रुबीले वार्षिक 10% साधारण ब्याजदरमा 2 वर्षका लागि एउटा ऋण लिइन् । यदि सो अवधिको ब्याज रु. 2,000 थियो भने:
  1. ब्याजको परिभाषा दिनुहोस् । [1]
  2. उनले जम्मा कति ऋण लिएकी थिइन् ? पत्ता लगाउनुहोस् । [2]
  3. ब्याज र साँवा बीचको अनुपात पत्ता लगाउनुहोस् । [1]
1. ब्याजको परिभाषा:
   साँवा (ऋण लिएको रकम) प्रयोग गरेबापत साहु वा बैंकलाई तिरिने अतिरिक्त रकमलाई ब्याज भनिन्छ ।
2. ऋण लिएको रकम (साँवा):
   समय (T) = 2 वर्ष
   दर (R) = 10%
   ब्याज (I) = रु. 2,000
   हामीलाई थाहा छ,
   साँवा (P) = \( \dfrac{I \times 100}{T \times R} = \dfrac{2,000 \times 100}{2 \times 10} = \dfrac{2,00,000}{20} = 10,000 \)
   तसर्थ, उनले रु. 10,000 ऋण लिएकी थिइन् ।
3. ब्याज र साँवा बीचको अनुपात:
   ब्याज = रु. 2,000
   साँवा = रु. 10,000
   यसरी,
   अनुपात = \( \dfrac{2,000}{10,000} = \dfrac{2}{10} = \dfrac{1}{5} \)
   तसर्थ, ब्याज र साँवा बीचको अनुपात 1:5 हो ।

Question 7

• Santosh borrowed a sum of Rs 7,000 from his friend Roopal. He paid an interest of Rs 1,400 to Roopal at the end of 2 years.
  1. Write the formula to find the rate of interest.[1]
  2. At which rate of interest did Santosh borrow the sum?[1]
  3. At the same rate of interest, calculate the interest for 5 years.[1]
  4. If Santosh had not paid any interest till the end of 5 years, how much amount would he need to clear the debt?[2]
1. Formula to find the rate of interest:
   Rate (R) = \( \dfrac{I \times 100}{P \times T} \)
2. Rate of interest:
   Principal (P) = Rs. 7,000
   Time (T) = 2 years
   Interest (I) = Rs. 1,400
   Thus,
   Rate (R) = \( \dfrac{1,400 \times 100}{7,000 \times 2} = 10\% \)
   So, the rate of interest is 10% per annum.
3. Interest for 5 years:
   Time (T) = 5 years
   Rate (R) = 10%
   Thus,
   Interest (I) = \( \dfrac{7,000 \times 5 \times 10}{100} = 3,500 \)
   So, the interest for 5 years is Rs. 3,500.
4. Amount to clear debt after 5 years:
   Principal (P) = Rs. 7,000
   Interest for 5 years (I) = Rs. 3,500
   Thus,
   Amount (A) = P + I = 7,000 + 3,500 = 10,500
   So, he would need Rs. 10,500 to clear the debt.
• सन्तोषले आफ्नी साथी रूपालबाट रु. 7,000 ऋण लिए । उनले 2 वर्षको अन्त्यमा रूपाललाई रु. 1,400 ब्याज तिरे भने:
  1. ब्याजको दर पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
  2. सन्तोषले कति ब्याजदरमा उक्त रकम ऋण लिएका थिए ? [1]
  3. सोही ब्याजदरमा, 5 वर्षको ब्याज गणना गर्नुहोस् । [1]
  4. यदि सन्तोषले 5 वर्षको अन्त्यसम्म कुनै पनि ब्याज नतिरेको भए, ऋण चुक्ता गर्न उनले जम्मा कति रकम तिर्नुपर्थ्यो ? [2]
1. ब्याजको दर पत्ता लगाउने सूत्र:
   दर (R) = \( \dfrac{I \times 100}{P \times T} \)
2. ब्याजको दर:
   साँवा (P) = रु. 7,000
   समय (T) = 2 वर्ष
   ब्याज (I) = रु. 1,400
   यसरी,
   दर (R) = \( \dfrac{1,400 \times 100}{7,000 \times 2} = \dfrac{1,40,000}{14,000} = 10\% \)
   तसर्थ, ब्याजको दर 10% प्रति वर्ष हो ।
3. 5 वर्षको ब्याज:
   समय (T) = 5 वर्ष
   दर (R) = 10%
   यसरी,
   ब्याज (I) = \( \dfrac{7,000 \times 5 \times 10}{100} = 3,500 \)
   तसर्थ, 5 वर्षको ब्याज रु. 3,500 हुन्छ ।
4. 5 वर्षपछिको जम्मा मिश्रधन:
   साँवा (P) = रु. 7,000
   5 वर्षको ब्याज (I) = रु. 3,500
   यसरी,
   मिश्रधन (A) = P + I = 7,000 + 3,500 = 10,500
   तसर्थ, ऋण चुक्ता गर्न उनले जम्मा रु. 10,500 तिर्नुपर्थ्यो ।

Question 8

• Ganesh borrowed a sum of Rs 27,000 from his friend Bishnu. He paid an interest of Rs 5,400 to Bishnu at the end of 2 years.
  1. Write the formula to find the rate of interest.[1]
  2. Find the rate of interest at which Ganesh borrowed the sum.[1]
  3. At the same rate of interest, calculate the interest for 3 years.[2]
  4. If Ganesh had not paid any interest till the end of 3 years, how much amount would be needed to clear the loan?[2]
1. Formula to find the rate of interest:
   Rate (R) = \( \dfrac{I \times 100}{P \times T} \)
2. Rate of interest:
   Principal (P) = Rs. 27,000
   Time (T) = 2 years
   Interest (I) = Rs. 5,400
   Thus,
   Rate (R) = \( \dfrac{5,400 \times 100}{27,000 \times 2} = 10\% \)
   So, the rate of interest is 10% per annum.
3. Interest for 3 years:
   Time (T) = 3 years
   Rate (R) = 10%
   Thus,
   Interest (I) = \( \dfrac{27,000 \times 3 \times 10}{100} = 8,100 \)
   So, the interest for 3 years is Rs. 8,100.
4. Amount to clear loan after 3 years:
   Principal (P) = Rs. 27,000
   Interest for 3 years (I) = Rs. 8,100
   Thus,
   Amount (A) = P + I = 27,000 + 8,100 = 35,100
   So, Rs. 35,100 would be needed to clear the loan.
• गणेशले आफ्ना साथी विष्णुबाट रु. 27,000 ऋण लिए । उनले 2 वर्षको अन्त्यमा विष्णुलाई रु. 5,400 ब्याज तिरे भने:
  1. ब्याजको दर पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
  2. गणेशले कति ब्याजदरमा उक्त रकम ऋण लिएका थिए ? पत्ता लगाउनुहोस् । [1]
  3. सोही ब्याजदरमा, 3 वर्षको ब्याज गणना गर्नुहोस् । [2]
  4. यदि गणेशले 3 वर्षको अन्त्यसम्म कुनै पनि ब्याज नतिरेको भए, ऋण चुक्ता गर्न उनले जम्मा कति रकम तिर्नुपर्थ्यो ? [2]
1. ब्याजको दर पत्ता लगाउने सूत्र:
   दर (R) = \( \dfrac{I \times 100}{P \times T} \)
2. ब्याजको दर:
   साँवा (P) = रु. 27,000
   समय (T) = 2 वर्ष
   ब्याज (I) = रु. 5,400
   यसरी,
   दर (R) = \( \dfrac{5,400 \times 100}{27,000 \times 2} = \dfrac{5,40,000}{54,000} = 10\% \)
   तसर्थ, ब्याजको दर 10% प्रति वर्ष हो ।
3. 3 वर्षको ब्याज:
   समय (T) = 3 वर्ष
   दर (R) = 10%
   यसरी,
   ब्याज (I) = \( \dfrac{27,000 \times 3 \times 10}{100} = 8,100 \)
   तसर्थ, 3 वर्षको ब्याज रु. 8,100 हुन्छ ।
4. 3 वर्षपछिको जम्मा मिश्रधन:
   साँवा (P) = रु. 27,000
   3 वर्षको ब्याज (I) = रु. 8,100
   यसरी,
   मिश्रधन (A) = P + I = 27,000 + 8,100 = 35,100
   तसर्थ, ऋण चुक्ता गर्न उनले जम्मा रु. 35,100 तिर्नुपर्थ्यो ।

Question 9

• A hotel of Mardi Himal has deposited Rs 5,00,000 in bank A and Rs 3,00,000 in bank B at the rate of 6% per annum.
  1. Write the formula to find simple interest.[1]
  2. How much interest does the hotel earn in 4 years from bank A?[1]
  3. Find the ratio of interest received from bank A and bank B in 4 years.[2]
1. Formula to find simple interest:
   Simple Interest (I) = \( \dfrac{P \times T \times R}{100} \)
2. Interest from Bank A:
   Principal (P) = Rs. 5,00,000
   Time (T) = 4 years
   Rate (R) = 6%
   Thus,
   Interest (I) = \( \dfrac{5,00,000 \times 4 \times 6}{100} = 1,20,000 \)
   So, the hotel earns Rs. 1,20,000 from Bank A.
3. Ratio of interest from Bank A and Bank B:
   Interest from Bank A (\(I_A\)) = Rs. 1,20,000
   Interest from Bank B (\(I_B\)) = \( \dfrac{3,00,000 \times 4 \times 6}{100} = 72,000 \)
   Thus,
   Ratio = \( \dfrac{1,20,000}{72,000} = \dfrac{5}{3} \)
   So, the ratio of interest received from Bank A and Bank B is 5:3.
• मर्दी हिमालको एउटा होटलले बैंक A मा रु. 5,00,000 र बैंक B मा रु. 3,00,000 वार्षिक 6% ब्याजदरमा जम्मा गरेको छ भने:
  1. साधारण ब्याज पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
  2. उक्त होटलले बैंक A बाट 4 वर्षमा कति ब्याज प्राप्त गर्छ ? [1]
  3. 4 वर्षमा बैंक A र बैंक B बाट प्राप्त हुने ब्याजको अनुपात पत्ता लगाउनुहोस् । [2]
1. साधारण ब्याज पत्ता लगाउने सूत्र:
   साधारण ब्याज (I) = \( \dfrac{P \times T \times R}{100} \)
2. बैंक A बाट प्राप्त ब्याज:
   साँवा (P) = रु. 5,00,000
   समय (T) = 4 वर्ष
   दर (R) = 6%
   यसरी,
   ब्याज (I) = \( \dfrac{5,00,000 \times 4 \times 6}{100} = 1,20,000 \)
   तसर्थ, होटलले बैंक A बाट रु. 1,20,000 ब्याज प्राप्त गर्छ ।
3. बैंक A र बैंक B को ब्याजको अनुपात:
   बैंक A को ब्याज (\(I_A\)) = रु. 1,20,000
   बैंक B को ब्याज (\(I_B\)) = \( \dfrac{3,00,000 \times 4 \times 6}{100} = 72,000 \)
   यसरी,
   अनुपात = \( \dfrac{1,20,000}{72,000} = \dfrac{120}{72} = \dfrac{5}{3} \)
   तसर्थ, बैंक A र बैंक B बाट प्राप्त हुने ब्याजको अनुपात 5:3 हो ।

Question 10

• The interest on Rs 5,040 in 5 years is Rs 2,520.
  1. Write the formula to find the simple interest if the amount (A) and principal (P) are given.[1]
  2. Find the rate of interest.[2]
  3. In how many years will the principal and interest be equal? Write with reason.[1]
1. Formula for Simple Interest:
   Simple Interest (I) = Amount (A) - Principal (P)
2. Rate of interest:
   Principal (P) = Rs. 5,040
   Time (T) = 5 years
   Interest (I) = Rs. 2,520
   We know,
   Rate (R) = \( \dfrac{I \times 100}{P \times T} = \dfrac{2,520 \times 100}{5,040 \times 5} = 10\% \)
   So, the rate of interest is 10% per annum.
3. Time for principal and interest to be equal:
   When Principal (P) and Interest (I) are equal, \( I = P \).
   We know, \( T = \dfrac{I \times 100}{P \times R} \).
   Since \( I = P \), then \( T = \dfrac{100}{R} = \dfrac{100}{10} = 10 \) years.
   Reason: Since the interest rate is 10% per year, it takes 10 years for the total interest to reach 100% of the principal (i.e., to become equal to the principal).
• रु. 5,040 को 5 वर्षको ब्याज रु. 2,520 हुन्छ भने:
  1. यदि मिश्रधन (A) र साँवा (P) दिइएको छ भने साधारण ब्याज पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
  2. ब्याजको दर पत्ता लगाउनुहोस् । [2]
  3. कति वर्षमा साँवा र ब्याज बराबर हुन्छन् ? कारणसहित लेख्नुहोस् । [1]
1. साधारण ब्याजको सूत्र:
   साधारण ब्याज (I) = मिश्रधन (A) - साँवा (P)
2. ब्याजको दर:
   साँवा (P) = रु. 5,040
   समय (T) = 5 वर्ष
   ब्याज (I) = रु. 2,520
   हामीलाई थाहा छ,
   दर (R) = \( \dfrac{I \times 100}{P \times T} = \dfrac{2,520 \times 100}{5,040 \times 5} = \dfrac{2,52,000}{25,200} = 10\% \)
   तसर्थ, ब्याजको दर 10% प्रति वर्ष हो ।
3. साँवा र ब्याज बराबर हुने समय:
   जब साँवा (P) र ब्याज (I) बराबर हुन्छन्, तब \( P = I \) हुन्छ ।
   हामीलाई थाहा छ, \( T = \dfrac{I \times 100}{P \times R} \)
   यहाँ \( I = P \) भएकाले, \( T = \dfrac{100}{R} = \dfrac{100}{10} = 10 \) वर्ष हुन्छ ।
   कारण: ब्याजको दर वार्षिक 10% भएकोले, 10 वर्षमा कुल ब्याज साँवाको 100% (अर्थात् साँवा बराबर) हुन्छ ।

Question 11

• Hari took a loan of Rs. 1,00,000 from a bank to go for abroad study at the rate of 12% p.a. simple interest. If he cleared the loan after 10 years then:
  1. Define amount.[1]
  2. What is the interest paid by him in 10 years?[2]
  3. If the interest rate was 10% p.a., what amount of money had he to pay in total?[2]
1. Definition of Amount:
   The sum of the principal and the interest earned on it over a certain period of time is called the amount. (i.e., Amount = Principal + Interest)
2. Interest for 10 years:
   Principal (P) = Rs. 1,00,000
   Time (T) = 10 years
   Rate (R) = 12%
   Thus,
   Interest (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{1,00,000 \times 10 \times 12}{100} = 1,20,000 \)
   So, the interest paid by him is Rs. 1,20,000.
3. Total amount to pay if the rate was 10%:
   New Rate (R) = 10%
   Interest (I) = \( \dfrac{1,00,000 \times 10 \times 10}{100} = 1,00,000 \)
   Total Amount (A) = P + I = 1,00,000 + 1,00,000 = 2,00,000
   So, he would have to pay a total of Rs. 2,00,000.
• हरिले वैदेशिक अध्ययनका लागि एउटा बैंकबाट वार्षिक 12% साधारण ब्याजदरमा रु. 1,00,000 ऋण लिए । यदि उनले 10 वर्षपछि उक्त ऋण चुक्ता गरे भने:
  1. मिश्रधन (Amount) को परिभाषा दिनुहोस् । [1]
  2. उनले 10 वर्षमा जम्मा कति ब्याज तिरे ? [2]
  3. यदि ब्याजदर वार्षिक 10% भएको भए, उनले जम्मा कति रकम (मिश्रधन) तिर्नुपर्थ्यो ? [2]
1. मिश्रधनको परिभाषा:
   साँवा र सो साँवामा निश्चित समयपछि प्राप्त हुने ब्याजको योगफललाई नै मिश्रधन भनिन्छ । (अर्थात्, मिश्रधन = साँवा + ब्याज)
2. 10 वर्षको ब्याज:
   साँवा (P) = रु. 1,00,000
   समय (T) = 10 वर्ष
   दर (R) = 12%
   यसरी,
   ब्याज (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{1,00,000 \times 10 \times 12}{100} = 1,20,000 \)
   तसर्थ, उनले 10 वर्षमा रु. 1,20,000 ब्याज तिरे ।
3. 10% ब्याजदर हुँदा तिर्नुपर्ने जम्मा रकम:
   नयाँ दर (R) = 10%
   ब्याज (I) = \( \dfrac{1,00,000 \times 10 \times 10}{100} = 1,00,000 \)
   जम्मा रकम (A) = P + I = 1,00,000 + 1,00,000 = 2,00,000
   तसर्थ, उनले जम्मा रु. 2,00,000 तिर्नुपर्थ्यो ।

Question 12

• Rajan deposited Rs. 60,000 at the rate of 10% p.a. in a savings account. After 5 years, he withdrew Rs. 40,000 and the total interest of 5 years.
  1. If interest (I), rate (R), and time (T) are given, write the formula to calculate the principal.[1]
  2. Find the interest of 5 years.[2]
  3. How long should he keep the remaining balance in the bank to get a total interest of Rs. 40,000 from the beginning?[2]
1. Formula to calculate principal:
   Principal (P) = \( \dfrac{I \times 100}{T \times R} \)
2. Interest of 5 years:
   Principal (P) = Rs. 60,000
   Time (T) = 5 years
   Rate (R) = 10%
   Thus,
   Interest (I) = \( \dfrac{60,000 \times 5 \times 10}{100} = 30,000 \)
   So, the interest for 5 years is Rs. 30,000.
3. Time for remaining balance:
   Interest already earned in 5 years = Rs. 30,000
   Total target interest = Rs. 40,000
   Remaining interest needed (I) = 40,000 - 30,000 = Rs. 10,000
   Remaining Principal (P) after withdrawal = 60,000 - 40,000 = Rs. 20,000
   Rate (R) = 10%
   Thus,
   Additional Time (T) = \( \dfrac{I \times 100}{P \times R} = \dfrac{10,000 \times 100}{20,000 \times 10} = 5 \) years
   So, he should keep the remaining balance for an additional 5 years (total 10 years from the beginning).
• राजानले एउटा बचत खातामा वार्षिक 10% ब्याजदरमा रु. 60,000 जम्मा गरे । 5 वर्षपछि उनले रु. 40,000 र 5 वर्षको जम्मा ब्याज झिके भने:
  1. यदि ब्याज (I), दर (R) र समय (T) दिइएको छ भने साँवा (P) गणना गर्ने सूत्र लेख्नुहोस् । [1]
  2. 5 वर्षको ब्याज पत्ता लगाउनुहोस् । [2]
  3. सुरुदेखि जम्मा रु. 40,000 ब्याज प्राप्त गर्न उनले बाँकी रहेको रकम कति समयसम्म बैंकमा राख्नुपर्छ ? [2]
1. साँवा गणना गर्ने सूत्र:
   साँवा (P) = \( \dfrac{I \times 100}{T \times R} \)
2. 5 वर्षको ब्याज:
   साँवा (P) = रु. 60,000
   समय (T) = 5 वर्ष
   दर (R) = 10%
   यसरी,
   ब्याज (I) = \( \dfrac{60,000 \times 5 \times 10}{100} = 30,000 \)
   तसर्थ, 5 वर्षको ब्याज रु. 30,000 हुन्छ ।
3. बाँकी ब्याज प्राप्त गर्न लाग्ने समय:
   उनले सुरुको 5 वर्षमा रु. 30,000 ब्याज पाइसकेका छन् ।
   लक्ष्य ब्याज = रु. 40,000
   बाँकी ब्याज पाउनुपर्ने (I) = 40,000 - 30,000 = रु. 10,000
   झिकेपछिको बाँकी साँवा (P) = 60,000 - 40,000 = रु. 20,000
   दर (R) = 10%
   यसरी,
   थप समय (T) = \( \dfrac{I \times 100}{P \times R} = \dfrac{10,000 \times 100}{20,000 \times 10} = 5 \) वर्ष
   तसर्थ, उनले बाँकी रकम थप 5 वर्ष (अर्थात् सुरुदेखि कुल 10 वर्ष) बैंकमा राख्नुपर्छ ।

Question 13

• Mina has deposited Rs. 4,00,000 in a commercial bank for 2 years at the rate of Rs. 10 interest per annum for Rs. 100.
  1. At what percent of interest rate per annum had Mina deposited the amount of money?[1]
  2. How much interest will Mina get in 2 years at the same rate of interest?[2]
  3. The ages of elder and younger daughters of Mina are 16 years and 12 years respectively. If Mina divides her Rs. 2,80,000 to her daughters based on the ratio of their ages, how much more money will the elder daughter get than the younger daughter?[2]
1. Interest rate in percentage:
   Since interest for Rs. 100 in 1 year is Rs. 10, the rate is 10%.
   So, Rate (R) = 10% p.a.
2. Interest for 2 years:
   Principal (P) = Rs. 4,00,000
   Time (T) = 2 years
   Rate (R) = 10%
   We know,
   Interest (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{4,00,000 \times 2 \times 10}{100} = 80,000 \)
   So, Mina will get Rs. 80,000 interest.
3. Division of money between daughters:
   Ratio of ages (Elder : Younger) = 16 : 12 = 4 : 3
   Sum of ratios = 4 + 3 = 7
   Total amount = Rs. 2,80,000
   Elder daughter's share = \( \dfrac{4}{7} \times 2,80,000 = 1,60,000 \)
   Younger daughter's share = \( \dfrac{3}{7} \times 2,80,000 = 1,20,000 \)
   Thus,
   Difference = 1,60,000 - 1,20,000 = 40,000
   So, the elder daughter will get Rs. 40,000 more than the younger daughter.
• मिनाले एउटा वाणिज्य बैंकमा रु. 100 को वार्षिक रु. 10 ब्याज पाउने गरी रु. 4,00,000 दुई वर्षका लागि जम्मा गरिन् भने:
  1. मिनाले वार्षिक कति प्रतिशत ब्याजदरमा उक्त रकम जम्मा गरेकी थिइन् ? [1]
  2. सोही ब्याजदरमा मिनाले 2 वर्षमा कति ब्याज प्राप्त गर्नेछिन् ? [2]
  3. मिनाका जेठी र कान्छी छोरीहरूको उमेर क्रमशः 16 वर्ष र 12 वर्ष छ । यदि मिनाले रु. 2,80,000 लाई आफ्ना छोरीहरूको उमेरको अनुपातको आधारमा बाँडिन् भने जेठी छोरीले कान्छी छोरीले भन्दा कति बढी रकम पाउँछिन् ? [2]
1. ब्याजदर प्रतिशतमा:
   रु. 100 को 1 वर्षको ब्याज रु. 10 हुनु भनेको ब्याजदर 10% हुनु हो ।
   तसर्थ, ब्याजदर (R) = 10% प्रति वर्ष ।
2. 2 वर्षको ब्याज:
   साँवा (P) = रु. 4,00,000
   समय (T) = 2 वर्ष
   दर (R) = 10%
   हामीलाई थाहा छ,
   ब्याज (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{4,00,000 \times 2 \times 10}{100} = 80,000 \)
   तसर्थ, मिनाले 2 वर्षमा रु. 80,000 ब्याज प्राप्त गर्नेछिन् ।
3. छोरीहरूका बीच रकमको बाँडफाँड:
   जेठी र कान्छी छोरीको उमेरको अनुपात = 16 : 12 = 4 : 3
   अनुपातको योग = 4 + 3 = 7
   जम्मा रकम = रु. 2,80,000
   जेठी छोरीले पाउने रकम = \( \dfrac{4}{7} \times 2,80,000 = 1,60,000 \)
   कान्छी छोरीले पाउने रकम = \( \dfrac{3}{7} \times 2,80,000 = 1,20,000 \)
   यसरी,
   रकमको फरक = 1,60,000 - 1,20,000 = 40,000
   तसर्थ, जेठी छोरीले कान्छी छोरीले भन्दा रु. 40,000 बढी पाउँछिन् ।

Question 14

• If Anju deposited Rs. 35,000 in a bank at the rate of 12% per year for 2 years.
  1. Write the formula to find Principal.[1]
  2. What interest does Anju get in 2 years?[1]
  3. Find the amount.[1]
1. Formula to find Principal:
   Principal (P) = \( \dfrac{I \times 100}{T \times R} \)
2. Interest for 2 years:
   Principal (P) = Rs. 35,000
   Time (T) = 2 years
   Rate (R) = 12%
   Thus,
   Interest (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{35,000 \times 2 \times 12}{100} = 8,400 \)
   So, Anju gets Rs. 8,400 as interest.
3. Find the amount:
   Principal (P) = Rs. 35,000
   Interest (I) = Rs. 8,400
   Thus,
   Amount (A) = P + I = 35,000 + 8,400 = 43,400
   So, the amount is Rs. 43,400.
• यदि अन्जुले एउटा बैंकमा वार्षिक 12% ब्याजदरमा 2 वर्षका लागि रु. 35,000 जम्मा गरिन् भने:
  1. साँवा (Principal) पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
  2. अन्जुले 2 वर्षमा कति ब्याज प्राप्त गर्छिन् ? [1]
  3. मिश्रधन (Amount) पत्ता लगाउनुहोस् । [1]
1. साँवा पत्ता लगाउने सूत्र:
   साँवा (P) = \( \dfrac{I \times 100}{T \times R} \)
2. 2 वर्षको ब्याज:
   साँवा (P) = रु. 35,000
   समय (T) = 2 वर्ष
   दर (R) = 12%
   यसरी,
   ब्याज (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{35,000 \times 2 \times 12}{100} = 8,400 \)
   तसर्थ, उनले रु. 8,400 ब्याज प्राप्त गर्छिन् ।
3. मिश्रधन:
   साँवा (P) = रु. 35,000
   ब्याज (I) = रु. 8,400
   यसरी,
   मिश्रधन (A) = P + I = 35,000 + 8,400 = 43,400
   तसर्थ, मिश्रधन रु. 43,400 हो ।

Question 15

• Mohan has deposited Rs. 2,50,000 in a bank at the rate of 8% per annum.
  1. Write the simple interest formula.[1]
  2. What does R stand for in the simple interest formula?[1]
  3. Find the interest amount obtained at the end of 3 years and 9 months.[2]
1. Simple Interest formula:
   Simple Interest (I) = \( \dfrac{P \times T \times R}{100} \)
2. Meaning of R:
   In the simple interest formula, 'R' stands for the Rate of Interest per annum.
3. Interest for 3 years and 9 months:
   Principal (P) = Rs. 2,50,000
   Rate (R) = 8%
   Time (T) = 3 years 9 months = \( 3 + \dfrac{9}{12} \) years = 3.75 years
   Thus,
   Interest (I) = \( \dfrac{2,50,000 \times 3.75 \times 8}{100} = 75,000 \)
   So, the interest amount obtained is Rs. 75,000.
• मोहनले वार्षिक 8% ब्याजदरमा एउटा बैंकमा रु. 2,50,000 जम्मा गरेका छन् भने:
  1. साधारण ब्याज पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
  2. साधारण ब्याजको सूत्रमा 'R' ले केलाई जनाउँछ ? [1]
  3. 3 वर्ष 9 महिनाको अन्त्यमा प्राप्त हुने ब्याज रकम पत्ता लगाउनुहोस् । [2]
1. साधारण ब्याजको सूत्र:
   साधारण ब्याज (I) = \( \dfrac{P \times T \times R}{100} \)
2. R को अर्थ:
   साधारण ब्याजको सूत्रमा 'R' ले ब्याजको वार्षिक दर (Rate of Interest per annum) लाई जनाउँछ ।
3. 3 वर्ष 9 महिनाको ब्याज:
   साँवा (P) = रु. 2,50,000
   दर (R) = 8%
   समय (T) = 3 वर्ष 9 महिना = \( 3 + \dfrac{9}{12} \) वर्ष = \( 3 + 0.75 \) वर्ष = 3.75 वर्ष
   यसरी,
   ब्याज (I) = \( \dfrac{2,50,000 \times 3.75 \times 8}{100} = 75,000 \)
   तसर्थ, उनले रु. 75,000 ब्याज प्राप्त गर्नेछन् ।

Question 16

• Roshani deposited Rs 40,000 in a bank to gain interest at the rate of 10% per annum for 18 months.
  1. Write the formula to find interest.[1]
  2. How much interest will she gain?[2]
  3. How much amount has to be returned to her by the bank?[1]
  4. If Roshani divides the interest she got to Manisha and Anushka in the ratio 2:3, how much money does each get?[2]
1. Formula to find interest:
   Interest (I) = \( \dfrac{P \times T \times R}{100} \)
2. Interest gained:
   Principal (P) = Rs. 40,000
   Rate (R) = 10%
   Time (T) = 18 months = \( \dfrac{18}{12} \) years = 1.5 years
   Thus,
   Interest (I) = \( \dfrac{40,000 \times 1.5 \times 10}{100} = 6,000 \)
   So, she will gain Rs. 6,000 as interest.
3. Total amount to be returned (Amount):
   Principal (P) = Rs. 40,000
   Interest (I) = Rs. 6,000
   Thus,
   Amount (A) = P + I = 40,000 + 6,000 = 46,000
   So, the bank has to return Rs. 46,000 to her.
4. Money received by Manisha and Anushka:
   Total Interest = Rs. 6,000
   Ratio = 2:3
   Sum of ratios = 2 + 3 = 5
   Thus,
   Manisha's share = \( \dfrac{2}{5} \times 6,000 = 2,400 \)
   Anushka's share = \( \dfrac{3}{5} \times 6,000 = 3,600 \)
   So, Manisha gets Rs. 2,400 and Anushka gets Rs. 3,600.
• रोशनीले वार्षिक 10% ब्याजदरमा 18 महिनाका लागि एउटा बैंकमा रु. 40,000 जम्मा गरिन् भने:
  1. ब्याज पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
  2. उनले कति ब्याज प्राप्त गर्नेछिन् ? [2]
  3. बैंकले उनलाई जम्मा कति रकम (मिश्रधन) फिर्ता गर्नुपर्छ ? [1]
  4. यदि रोशनीले प्राप्त गरेको ब्याजलाई मनिषा र अनुष्काका बीच 2:3 को अनुपातमा बाँडिन् भने, प्रत्येकले कति-कति रकम पाउँछन् ? [2]
1. ब्याज पत्ता लगाउने सूत्र:
   ब्याज (I) = \( \dfrac{P \times T \times R}{100} \)
2. प्राप्त हुने ब्याज:
   साँवा (P) = रु. 40,000
   दर (R) = 10%
   समय (T) = 18 महिना = \( \dfrac{18}{12} \) वर्ष = 1.5 वर्ष
   यसरी,
   ब्याज (I) = \( \dfrac{40,000 \times 1.5 \times 10}{100} = 6,000 \)
   तसर्थ, उनले रु. 6,000 ब्याज प्राप्त गर्नेछिन् ।
3. बैंकले फिर्ता गर्नुपर्ने जम्मा रकम (मिश्रधन):
   साँवा (P) = रु. 40,000
   ब्याज (I) = रु. 6,000
   यसरी,
   मिश्रधन (A) = P + I = 40,000 + 6,000 = 46,000
   तसर्थ, बैंकले उनलाई रु. 46,000 फिर्ता गर्नुपर्छ ।
4. मनिषा र अनुष्काले पाउने रकम:
   बाँडिने ब्याज = रु. 6,000
   अनुपात = 2:3
   अनुपातको योग = 2 + 3 = 5
   यसरी,
   मनिषाले पाउने रकम = \( \dfrac{2}{5} \times 6,000 = 2,400 \)
   अनुष्काले पाउने रकम = \( \dfrac{3}{5} \times 6,000 = 3,600 \)
   तसर्थ, मनिषाले रु. 2,400 र अनुष्काले रु. 3,600 पाउँछन् ।

Question 17

• The simple interest on Rs 4,000 for 5 years is Rs 2,400.
  1. If principal (P), time (T), and rate of interest (R) are given, write the formula to find interest (I).[1]
  2. Find the rate of interest.[2]
  3. At the same interest rate, how much will be the interest on Rs 2,000 for 4 years?[2]
1. Formula to find interest:
   Simple Interest (I) = \( \dfrac{P \times T \times R}{100} \)
2. Rate of interest:
   Principal (P) = Rs. 4,000
   Time (T) = 5 years
   Interest (I) = Rs. 2,400
   We know,
   Rate (R) = \( \dfrac{I \times 100}{P \times T} = \dfrac{2,400 \times 100}{4,000 \times 5} = 12\% \)
   So, the rate of interest is 12% per annum.
3. Calculation of new interest:
   New Principal (P) = Rs. 2,000
   New Time (T) = 4 years
   Rate (R) = 12%
   Thus,
   Interest (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{2,000 \times 4 \times 12}{100} = 960 \)
   So, the interest on Rs. 2,000 for 4 years will be Rs. 960.
• रु. 4,000 को 5 वर्षको साधारण ब्याज रु. 2,400 हुन्छ भने:
  1. यदि साँवा (P), समय (T) र ब्याजदर (R) दिइएको छ भने, ब्याज (I) पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
  2. ब्याजको दर पत्ता लगाउनुहोस् । [2]
  3. सोही ब्याजदरमा, रु. 2,000 को 4 वर्षको ब्याज कति हुन्छ ? [2]
1. ब्याज पत्ता लगाउने सूत्र:
   साधारण ब्याज (I) = \( \dfrac{P \times T \times R}{100} \)
2. ब्याजको दर:
   साँवा (P) = रु. 4,000
   समय (T) = 5 वर्ष
   ब्याज (I) = रु. 2,400
   हामीलाई थाहा छ,
   दर (R) = \( \dfrac{I \times 100}{P \times T} = \dfrac{2,400 \times 100}{4,000 \times 5} = \dfrac{2,40,000}{20,000} = 12\% \)
   तसर्थ, ब्याजको दर 12% प्रति वर्ष हो ।
3. नयाँ ब्याज गणना:
   नयाँ साँवा (P) = रु. 2,000
   नयाँ समय (T) = 4 वर्ष
   दर (R) = 12%
   यसरी,
   ब्याज (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{2,000 \times 4 \times 12}{100} = 960 \)
   तसर्थ, रु. 2,000 को 4 वर्षको ब्याज रु. 960 हुन्छ ।

Question 18

• Ramesh gave Suresh a loan of Rs 24,500 at a fixed simple interest rate for 2 years. After the term ended, Suresh repaid a total amount of Rs 30,380.
  1. Write the formula to find simple interest when principal (P), time (T), and rate of interest (R) are given.[1]
  2. Find the interest rate paid by Suresh.[1]
  3. How much amount is returned by Suresh to Ramesh, if he paid at the end of 3 years?[2]
  4. If Ramesh distributes the total amount he received in two years between Ganesh and Mahesh in the ratio 3:7, who will receive how much more?[2]
1. Simple Interest formula:
   Simple Interest (I) = \( \dfrac{P \times T \times R}{100} \)
2. Rate of interest:
   Principal (P) = Rs. 24,500
   Amount (A) = Rs. 30,380
   Interest (I) = A - P = 30,380 - 24,500 = Rs. 5,880
   Time (T) = 2 years
   Thus,
   Rate (R) = \( \dfrac{I \times 100}{P \times T} = \dfrac{5,880 \times 100}{24,500 \times 2} = 12\% \)
   So, the interest rate is 12% per annum.
3. Total amount after 3 years:
   Time (T) = 3 years
   Interest (I) = \( \dfrac{24,500 \times 3 \times 12}{100} = 8,820 \)
   Thus,
   Amount (A) = P + I = 24,500 + 8,820 = 33,320
   So, the amount returned after 3 years would be Rs. 33,320.
4. Distribution between Ganesh and Mahesh:
   Total Amount = Rs. 30,380
   Ratio = 3:7 (Ganesh : Mahesh)
   Sum of ratios = 3 + 7 = 10
   Ganesh's share = \( \dfrac{3}{10} \times 30,380 = 9,114 \)
   Mahesh's share = \( \dfrac{7}{10} \times 30,380 = 21,266 \)
   Thus,
   Difference = 21,266 - 9,114 = 12,152
   So, Mahesh will receive Rs. 12,152 more than Ganesh.
• रमेशले सुरेशलाई रु. 24,500 निश्चित साधारण ब्याजदरमा 2 वर्षका लागि ऋण दिए । समय सीमा सकिएपछि सुरेशले जम्मा रु. 30,380 फिर्ता गरे भने:
  1. साँवा (P), समय (T) र ब्याजदर (R) दिइएको अवस्थामा साधारण ब्याज पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
  2. सुरेशले तिरेको ब्याजको दर पत्ता लगाउनुहोस् । [1]
  3. यदि सुरेशले 3 वर्षको अन्त्यमा रकम फिर्ता गरेको भए, उनले रमेशलाई जम्मा कति रकम (मिश्रधन) बुझाउनुपर्थ्यो ? [2]
  4. यदि रमेशले 2 वर्षमा प्राप्त गरेको जम्मा रकमलाई गणेश र महेशका बीच 3:7 को अनुपातमा बाँडे भने, कसले कति रकम बढी पाउँछन् ? [2]
1. साधारण ब्याजको सूत्र:
   साधारण ब्याज (I) = \( \dfrac{P \times T \times R}{100} \)
2. ब्याजको दर:
   साँवा (P) = रु. 24,500
   मिश्रधन (A) = रु. 30,380
   ब्याज (I) = A - P = 30,380 - 24,500 = रु. 5,880
   समय (T) = 2 वर्ष
   यसरी,
   दर (R) = \( \dfrac{I \times 100}{P \times T} = \dfrac{5,880 \times 100}{24,500 \times 2} = 12\% \)
   तसर्थ, ब्याजको दर 12% प्रति वर्ष हो ।
3. 3 वर्षपछिको जम्मा रकम (मिश्रधन):
   समय (T) = 3 वर्ष
   ब्याज (I) = \( \dfrac{24,500 \times 3 \times 12}{100} = 8,820 \)
   यसरी,
   मिश्रधन (A) = P + I = 24,500 + 8,820 = 33,320
   तसर्थ, 3 वर्षमा उनले रु. 33,320 फिर्ता गर्नुपर्थ्यो ।
4. गणेश र महेशका बीचको बाँडफाँड:
   जम्मा रकम = रु. 30,380
   अनुपात = 3:7 (गणेश : महेश)
   अनुपातको योग = 3 + 7 = 10
   गणेशले पाउने = \( \dfrac{3}{10} \times 30,380 = 9,114 \)
   महेशले पाउने = \( \dfrac{7}{10} \times 30,380 = 21,266 \)
   यसरी,
   फरक = 21,266 - 9,114 = 12,152
   तसर्थ, महेशले गणेशको भन्दा रु. 12,152 बढी पाउँछन् ।

Question 19

• If principal P = Rs 10,000, time T = 4 years, and rate R = 6% per annum, then:
  1. Write the formula to find simple interest.[1]
  2. Find the interest amount.[1]
  3. Find the total amount.[1]
1. Formula to find simple interest:
   Simple Interest (I) = \( \dfrac{P \times T \times R}{100} \)
2. Interest amount:
   Principal (P) = Rs. 10,000
   Time (T) = 4 years
   Rate (R) = 6%
   Thus,
   Interest (I) = \( \dfrac{10,000 \times 4 \times 6}{100} = 2,400 \)
   So, the interest amount is Rs. 2,400.
3. Total amount:
   Principal (P) = Rs. 10,000
   Interest (I) = Rs. 2,400
   Thus,
   Amount (A) = P + I = 10,000 + 2,400 = 12,400
   So, the total amount is Rs. 12,400.
• यदि साँवा (P) = रु. 10,000, समय (T) = 4 वर्ष र ब्याजदर (R) = 6% वार्षिक छ भने:
  1. साधारण ब्याज पत्ता लगाउने सूत्र लेख्नुहोस् । [1]
  2. ब्याज रकम पत्ता लगाउनुहोस् । [1]
  3. जम्मा मिश्रधन पत्ता लगाउनुहोस् । [1]
1. साधारण ब्याजको सूत्र:
   साधारण ब्याज (I) = \( \dfrac{P \times T \times R}{100} \)
2. ब्याज रकम:
   साँवा (P) = रु. 10,000
   समय (T) = 4 वर्ष
   दर (R) = 6%
   यसरी,
   ब्याज (I) = \( \dfrac{10,000 \times 4 \times 6}{100} = 2,400 \)
   तसर्थ, ब्याज रकम रु. 2,400 हो ।
3. जम्मा मिश्रधन:
   साँवा (P) = रु. 10,000
   ब्याज (I) = रु. 2,400
   यसरी,
   मिश्रधन (A) = P + I = 10,000 + 2,400 = 12,400
   तसर्थ, जम्मा मिश्रधन रु. 12,400 हो ।

Question 20

• Ram has deposited Rs 20,000 in an Agricultural Development Bank for 5 years at the rate of Rs 12 interest per annum for Rs 100.
  1. At what percent of interest rate per annum has Ram deposited the amount of money?[1]
  2. How much interest will Ram get in 5 years at the same rate of interest?[2]
  3. The ages of Ram’s two sons are 8 years and 12 years respectively. He divides Rs 20,000 between his sons in the ratio of their ages. How much does each get?[2]
1. Interest rate in percentage:
   Since the interest for Rs 100 in 1 year is Rs 12, the rate is 12%.
   So, Rate (R) = 12% p.a.
2. Interest for 5 years:
   Principal (P) = Rs 20,000
   Time (T) = 5 years
   Rate (R) = 12%
   We know,
   Interest (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{20,000 \times 5 \times 12}{100} = 12,000 \)
   So, Ram will get Rs 12,000 interest.
3. Division of money between sons:
   Ratio of their ages = 8 : 12 = 2 : 3
   Sum of ratios = 2 + 3 = 5
   Total amount = Rs 20,000
   Younger son's share (8 yrs) = \( \dfrac{2}{5} \times 20,000 = 8,000 \)
   Elder son's share (12 yrs) = \( \dfrac{3}{5} \times 20,000 = 12,000 \)
   So, the younger son gets Rs 8,000 and the elder son gets Rs 12,000.
• रामले कृषि विकास बैंकमा रु. 100 को वार्षिक रु. 12 ब्याज पाउने गरी रु. 20,000 पाँच वर्षका लागि जम्मा गरे भने:
  1. रामले वार्षिक कति प्रतिशत ब्याजदरमा उक्त रकम जम्मा गरेका थिए ? [1]
  2. सोही ब्याजदरमा रामले 5 वर्षमा कति ब्याज प्राप्त गर्नेछन् ? [2]
  3. रामका दुई छोराहरूको उमेर क्रमशः 8 वर्ष र 12 वर्ष छ । उनले रु. 20,000 लाई छोराहरूको उमेरको अनुपातमा बाँडे भने प्रत्येकले कति-कति रकम पाउँछन् ? [2]
1. ब्याजदर प्रतिशतमा:
   रु. 100 को 1 वर्षको ब्याज रु. 12 हुनु भनेको ब्याजदर 12% हुनु हो ।
   तसर्थ, ब्याजदर (R) = 12% प्रति वर्ष ।
2. 5 वर्षको ब्याज:
   साँवा (P) = रु. 20,000
   समय (T) = 5 वर्ष
   दर (R) = 12%
   हामीलाई थाहा छ,
   ब्याज (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{20,000 \times 5 \times 12}{100} = 12,000 \)
   तसर्थ, रामले 5 वर्षमा रु. 12,000 ब्याज प्राप्त गर्नेछन् ।
3. छोराहरूका बीच रकमको बाँडफाँड:
   छोराहरूको उमेरको अनुपात = 8 : 12 = 2 : 3
   अनुपातको योग = 2 + 3 = 5
   जम्मा रकम = रु. 20,000
   कान्छो छोरा (8 वर्ष) ले पाउने रकम = \( \dfrac{2}{5} \times 20,000 = 8,000 \)
   जेठो छोरा (12 वर्ष) ले पाउने रकम = \( \dfrac{3}{5} \times 20,000 = 12,000 \)
   तसर्थ, कान्छो छोराले रु. 8,000 र जेठो छोराले रु. 12,000 पाउँछन् ।

Question 21

• Shriyansh deposited Rs 25,000 in a bank at the rate of 10% per annum simple interest for 2 years.
  1. What do you mean by rate of interest 10% per annum?[1]
  2. Find the interest for 2 years.[1]
1. Meaning of 10% interest per annum:
   Rate of interest 10% per annum means that Rs. 10 is paid as interest for every Rs. 100 of the principal amount for a period of one year.
2. Interest for 2 years:
   Principal (P) = Rs. 25,000
   Time (T) = 2 years
   Rate (R) = 10%
   We know,
   Interest (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{25,000 \times 2 \times 10}{100} = 5,000 \)
   So, the interest for 2 years is Rs. 5,000.
• श्रियान्सले वार्षिक 10% साधारण ब्याजदरमा 2 वर्षका लागि एउटा बैंकमा रु. 25,000 जम्मा गरे भने:
  1. वार्षिक 10% ब्याजदर भन्नाले के बुझिन्छ ? [1]
  2. 2 वर्षको ब्याज पत्ता लगाउनुहोस् । [1]
1. वार्षिक 10% ब्याजदरको अर्थ:
   वार्षिक 10% ब्याजदर भन्नाले रु. 100 साँवाको एक वर्षमा रु. 10 ब्याज प्राप्त हुन्छ भन्ने बुझिन्छ ।
2. 2 वर्षको ब्याज:
   साँवा (P) = रु. 25,000
   समय (T) = 2 वर्ष
   दर (R) = 10%
   हामीलाई थाहा छ,
   ब्याज (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{25,000 \times 2 \times 10}{100} = 5,000 \)
   तसर्थ, 2 वर्षको ब्याज रु. 5,000 हुन्छ ।

Question 22

• If Karuna has deposited Rs 35,000 in a bank at 12% rate of interest per year for 2 years,
  1. Express the simple interest in the form of P, T, and R.[1]
  2. Find the interest.[1]
  3. Divide the interest in the ratio 1:2.[2]
1. Simple Interest formula:
   Simple Interest (I) = \( \dfrac{P \times T \times R}{100} \)
2. Find the interest:
   Principal (P) = Rs. 35,000
   Time (T) = 2 years
   Rate (R) = 12%
   Thus,
   Interest (I) = \( \dfrac{35,000 \times 2 \times 12}{100} = 8,400 \)
   So, the interest is Rs. 8,400.
3. Divide the interest (Ratio 1:2):
   Total Interest = Rs. 8,400
   Sum of ratios = 1 + 2 = 3
   First part = \( \dfrac{1}{3} \times 8,400 = 2,800 \)
   Second part = \( \dfrac{2}{3} \times 8,400 = 5,600 \)
   So, the divided amounts are Rs. 2,800 and Rs. 5,600.
• यदि करुणाले एउटा बैंकमा वार्षिक 12% ब्याजदरमा 2 वर्षका लागि रु. 35,000 जम्मा गरेकी छिन् भने:
  1. साधारण ब्याजलाई P, T र R को रूपमा व्यक्त गर्नुहोस् । [1]
  2. ब्याज पत्ता लगाउनुहोस् । [1]
  3. प्राप्त ब्याजलाई 1:2 को अनुपातमा विभाजन गर्नुहोस् । [2]
1. साधारण ब्याजको सूत्र:
   साधारण ब्याज (I) = \( \dfrac{P \times T \times R}{100} \)
2. ब्याज गणना:
   साँवा (P) = रु. 35,000
   समय (T) = 2 वर्ष
   दर (R) = 12%
   यसरी,
   ब्याज (I) = \( \dfrac{35,000 \times 2 \times 12}{100} = 8,400 \)
   तसर्थ, ब्याज रु. 8,400 हुन्छ ।
3. ब्याजको विभाजन (अनुपात 1:2):
   जम्मा ब्याज = रु. 8,400
   अनुपातको योग = 1 + 2 = 3
   पहिलो भाग = \( \dfrac{1}{3} \times 8,400 = 2,800 \)
   दोस्रो भाग = \( \dfrac{2}{3} \times 8,400 = 5,600 \)
   तसर्थ, विभाजित रकमहरू रु. 2,800 र रु. 5,600 हुन् ।

Question 23

• Rs 6,000 is lent out at the rate of \(12\dfrac{1}{2}\%\) per annum for 10 months.
  1. How much interest does Sangita earn in 10 months?[1]
  2. How much amount will Sangita receive after 2 years at the same rate?[2]
  3. The ages of Sangita’s elder and younger brothers are 12 years and 8 years respectively. If she divides Rs 200,000 between them in the ratio of their ages, how much more will the elder brother receive?[2]
1. Interest for 10 months:
   Principal (P) = Rs. 6,000
   Rate (R) = \(12.5\%\)
   Time (T) = 10 months = \( \dfrac{10}{12} \) years
   Thus,
   Interest (I) = \( \dfrac{6,000 \times \frac{10}{12} \times 12.5}{100} = 625 \)
   So, Sangita earns Rs. 625 interest.
2. Amount after 2 years:
   Principal (P) = Rs. 6,000
   Time (T) = 2 years
   Rate (R) = 12.5%
   Interest (I) = \( \dfrac{6,000 \times 2 \times 12.5}{100} = 1,500 \)
   Amount (A) = P + I = 6,000 + 1,500 = 7,500
   So, Sangita will receive Rs. 7,500.
3. Distribution between brothers:
   Ratio of ages (Elder : Younger) = 12 : 8 = 3 : 2
   Sum of ratios = 3 + 2 = 5
   Total amount = Rs. 200,000
   Elder brother's share = \( \dfrac{3}{5} \times 200,000 = 120,000 \)
   Younger brother's share = \( \dfrac{2}{5} \times 200,000 = 80,000 \)
   Difference = 120,000 - 80,000 = 40,000
   So, the elder brother will receive Rs. 40,000 more.
• रु. 6,000 लाई वार्षिक \(12\dfrac{1}{2}\%\) ब्याजदरमा 10 महिनाका लागि ऋण दिइएको छ भने:
  1. सङ्गिताले 10 महिनामा कति ब्याज प्राप्त गर्छिन् ? [1]
  2. सोही दरमा 2 वर्षपछि सङ्गिताले जम्मा कति रकम (मिश्रधन) प्राप्त गर्नेछिन् ? [2]
  3. सङ्गिताका जेठो र कान्छो भाइहरूको उमेर क्रमशः 12 वर्ष र 8 वर्ष छ । यदि उनले रु. 2,00,000 लाई उनीहरूको उमेरको अनुपातमा बाँडिन् भने जेठो भाइले कान्छो भाइले भन्दा कति बढी रकम पाउँछ ? [2]
1. 10 महिनाको ब्याज:
   साँवा (P) = रु. 6,000
   दर (R) = \(12\dfrac{1}{2}\%\) = 12.5%
   समय (T) = 10 महिना = \( \dfrac{10}{12} \) वर्ष
   यसरी,
   ब्याज (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{6,000 \times \frac{10}{12} \times 12.5}{100} = \dfrac{500 \times 1.25}{1} = 625 \)
   तसर्थ, उनले रु. 625 ब्याज प्राप्त गर्छिन् ।
2. 2 वर्षपछिको मिश्रधन:
   साँवा (P) = रु. 6,000
   समय (T) = 2 वर्ष
   दर (R) = 12.5%
   ब्याज (I) = \( \dfrac{6,000 \times 2 \times 12.5}{100} = 1,500 \)
   मिश्रधन (A) = P + I = 6,000 + 1,500 = 7,500
   तसर्थ, उनले रु. 7,500 प्राप्त गर्नेछिन् ।
3. भाइहरूका बीचको बाँडफाँड:
   उमेरको अनुपात (जेठो : कान्छो) = 12 : 8 = 3 : 2
   अनुपातको योग = 3 + 2 = 5
   जम्मा रकम = रु. 2,00,000
   जेठो भाइले पाउने = \( \dfrac{3}{5} \times 2,00,000 = 1,20,000 \)
   कान्छो भाइले पाउने = \( \dfrac{2}{5} \times 2,00,000 = 80,000 \)
   रकमको फरक = 1,20,000 - 80,000 = 40,000
   तसर्थ, जेठो भाइले रु. 40,000 बढी पाउँछ ।

Question 24

• Ram’s monthly income is Rs 40,000. The ratio of his saving to expenditure in a month is 2:3.
  1. In which month does he get an income of Rs 40,000? Find it.[1]
  2. How much amount does he save in a month? Find it.[2]
  3. By how much should Ram’s yearly expenditure be reduced to maintain a yearly expenditure of Rs 2,70,000 only?[2]
  4. How much simple interest will Ram get if he deposits his monthly saving amount in a bank at 10% interest rate for 2 years?[1]
1. Month of income:
   Since the question states "monthly income", he gets an income of Rs 40,000 in every month of the year.
2. Monthly Saving:
   Income = Rs. 40,000
   Ratio (Saving : Expenditure) = 2:3
   Sum of ratios = 2 + 3 = 5
   Thus,
   Monthly Saving = \( \dfrac{2}{5} \times 40,000 = 16,000 \)
   So, he saves Rs. 16,000 in a month.
3. Reduction in yearly expenditure:
   Monthly Expenditure = \( \dfrac{3}{5} \times 40,000 = 24,000 \)
   Current Yearly Expenditure = 24,000 × 12 = Rs. 2,88,000
   Target Yearly Expenditure = Rs. 2,70,000
   Thus,
   Reduction needed = 2,88,000 - 2,70,000 = 18,000
   So, his yearly expenditure should be reduced by Rs. 18,000.
4. Simple Interest:
   Principal (Monthly saving P) = Rs. 16,000
   Time (T) = 2 years
   Rate (R) = 10%
   Thus,
   Interest (I) = \( \dfrac{16,000 \times 2 \times 10}{100} = 3,200 \)
   So, Ram will get Rs. 3,200 as simple interest.
• रामको मासिक आम्दानी रु. 40,000 छ । उनको एक महिनाको बचत र खर्चको अनुपात 2:3 छ भने:
  1. उनले कुन महिनामा रु. 40,000 आम्दानी गर्छन् ? पत्ता लगाउनुहोस् । [1]
  2. उनले एक महिनामा कति रकम बचत गर्छन् ? पत्ता लगाउनुहोस् । [2]
  3. वार्षिक खर्च रु. 2,70,000 मात्र कायम गर्न रामको वार्षिक खर्चमा कतिले कमी ल्याउनुपर्छ ? [2]
  4. यदि रामले आफ्नो मासिक बचत रकमलाई वार्षिक 10% ब्याजदरमा 2 वर्षका लागि बैंकमा जम्मा गरे भने उनले कति साधारण ब्याज पाउँछन् ? [1]
1. आम्दानी हुने महिना:
   प्रश्नमा "मासिक आम्दानी" भनिएकोले उनले प्रत्येक महिना (वर्षको १२ वटै महिना) रु. 40,000 आम्दानी गर्छन् ।
2. मासिक बचत:
   आम्दानी = रु. 40,000
   बचत र खर्चको अनुपात = 2:3
   अनुपातको योग = 2 + 3 = 5
   यसरी,
   मासिक बचत = \( \dfrac{2}{5} \times 40,000 = 16,000 \)
   तसर्थ, उनले एक महिनामा रु. 16,000 बचत गर्छन् ।
3. वार्षिक खर्चमा ल्याउनुपर्ने कमी:
   मासिक खर्च = \( \dfrac{3}{5} \times 40,000 = 24,000 \)
   हालको वार्षिक खर्च = 24,000 × 12 = रु. 2,88,000
   कायम गर्नुपर्ने खर्च = रु. 2,70,000
   यसरी,
   खर्चमा ल्याउनुपर्ने कमी = 2,88,000 - 2,70,000 = 18,000
   तसर्थ, वार्षिक खर्चमा रु. 18,000 ले कमी ल्याउनुपर्छ ।
4. ब्याज गणना:
   साँवा (मासिक बचत P) = रु. 16,000
   समय (T) = 2 वर्ष
   दर (R) = 10%
   यसरी,
   ब्याज (I) = \( \dfrac{16,000 \times 2 \times 10}{100} = 3,200 \)
   तसर्थ, उनले रु. 3,200 ब्याज पाउँछन् ।

Question 25

• Rina took a loan of Rs 50,000 from Pawan at 18% per annum simple interest for 3 years.
  1. How much simple interest is paid by Rina in 3 years? Find it.[1]
  2. Find the total amount of principal and interest to be paid by Rina.[1]
  3. If Rina took the loan at 12% per annum, then how much less interest would she have to pay?[2]
1. Interest paid in 3 years:
   Principal (P) = Rs. 50,000
   Time (T) = 3 years
   Rate (R) = 18%
   We know,
   Interest (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{50,000 \times 3 \times 18}{100} = 27,000 \)
   So, Rina has to pay Rs. 27,000 as interest.
2. Total amount to be paid:
   Amount (A) = Principal (P) + Interest (I)
   A = 50,000 + 27,000 = 77,000
   So, the total amount to be paid is Rs. 77,000.
3. Difference in interest if rate was 12%:
   Original Rate = 18%, New Rate = 12%
   Difference in Rate = 18% - 12% = 6%
   Thus,
   Interest saved = \( \dfrac{50,000 \times 3 \times 6}{100} = 9,000 \)
   So, she would have to pay Rs. 9,000 less interest.
• रिनाले पवनबाट वार्षिक 18% साधारण ब्याजदरमा 3 वर्षका लागि रु. 50,000 ऋण लिइन् भने:
  1. रिनाले 3 वर्षमा कति साधारण ब्याज तिर्नुपर्छ ? पत्ता लगाउनुहोस् । [1]
  2. रिनाले तिर्नुपर्ने साँवा र ब्याजको जम्मा रकम (मिश्रधन) पत्ता लगाउनुहोस् । [1]
  3. यदि रिनाले वार्षिक 12% ब्याजदरमा ऋण लिएकी भए, उनले कति कम ब्याज तिर्नुपर्थ्यो ? [2]
1. 3 वर्षको ब्याज:
   साँवा (P) = रु. 50,000
   समय (T) = 3 वर्ष
   दर (R) = 18%
   हामीलाई थाहा छ,
   ब्याज (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{50,000 \times 3 \times 18}{100} = 27,000 \)
   तसर्थ, रिनाले रु. 27,000 ब्याज तिर्नुपर्छ ।
2. जम्मा मिश्रधन:
   मिश्रधन (A) = साँवा (P) + ब्याज (I)
   A = 50,000 + 27,000 = 77,000
   तसर्थ, रिनाले तिर्नुपर्ने जम्मा रकम रु. 77,000 हो ।
3. ब्याजमा हुने बचत:
   पुरानो दर = 18%, नयाँ दर = 12%
   दरको फरक = 18% - 12% = 6%
   यसरी,
   कम तिर्नुपर्ने ब्याज = \( \dfrac{50,000 \times 3 \times 6}{100} = 9,000 \)
   तसर्थ, उनले रु. 9,000 कम ब्याज तिर्नुपर्थ्यो ।

Question 26

• Sarita invested Rs 5,000 as a loan and lent it to Mansur for 3 years at 10% simple interest per annum.
  1. How much interest is obtained by Sarita?[1]
  2. How long should Sarita wait to get double the invested sum?[2]
  3. What will be the interest on Rs 12,000 at the same rate and for the same time?[1]
1. Interest obtained:
   Principal (P) = Rs. 5,000
   Time (T) = 3 years
   Rate (R) = 10%
   We know,
   Interest (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{5,000 \times 3 \times 10}{100} = 1,500 \)
   So, Sarita obtains Rs. 1,500 as interest.
2. Time to double the sum:
   To double the sum, the Interest (I) must be equal to the Principal (P).
   Here, I = P = Rs. 5,000
   Rate (R) = 10%
   Thus,
   Time (T) = \( \dfrac{I \times 100}{P \times R} = \dfrac{5,000 \times 100}{5,000 \times 10} = 10 \) years
   So, Sarita should wait 10 years to double her investment.
3. Interest on Rs. 12,000:
   New Principal (P) = Rs. 12,000
   Time (T) = 3 years
   Rate (R) = 10%
   Thus,
   Interest (I) = \( \dfrac{12,000 \times 3 \times 10}{100} = 3,600 \)
   So, the interest on Rs. 12,000 will be Rs. 3,600.
• सरिताले रु. 5,000 ऋणको रूपमा लगानी गरिन् र मन्सुरलाई वार्षिक 10% साधारण ब्याजदरमा 3 वर्षका लागि दिइन् भने:
  1. सरिताले कति ब्याज प्राप्त गर्छिन् ? [1]
  2. आफ्नो लगानी गरिएको रकम दोब्बर हुन सरिताले कति समय कुर्नुपर्छ ? [2]
  3. सोही दर र सोही समयमा रु. 12,000 को ब्याज कति हुन्छ ? [1]
1. ब्याज गणना:
   साँवा (P) = रु. 5,000
   समय (T) = 3 वर्ष
   दर (R) = 10%
   हामीलाई थाहा छ,
   ब्याज (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{5,000 \times 3 \times 10}{100} = 1,500 \)
   तसर्थ, सरिताले रु. 1,500 ब्याज प्राप्त गर्छिन् ।
2. रकम दोब्बर हुन लाग्ने समय:
   रकम दोब्बर हुन ब्याज (I) साँवा (P) सँग बराबर हुनुपर्छ ।
   यहाँ, I = P = रु. 5,000
   दर (R) = 10%
   यसरी,
   समय (T) = \( \dfrac{I \times 100}{P \times R} = \dfrac{5,000 \times 100}{5,000 \times 10} = 10 \) वर्ष
   तसर्थ, रकम दोब्बर हुन सरिताले 10 वर्ष कुर्नुपर्छ ।
3. नयाँ ब्याज गणना:
   नयाँ साँवा (P) = रु. 12,000
   समय (T) = 3 वर्ष
   दर (R) = 10%
   यसरी,
   ब्याज (I) = \( \dfrac{12,000 \times 3 \times 10}{100} = 3,600 \)
   तसर्थ, रु. 12,000 को ब्याज रु. 3,600 हुन्छ ।

Question 27

• Sunil has deposited RS 300,000 in Rastriya Banijya Bank for 3 years at the rate of Rs 12 simple interest per annum for every Rs 100.
  1. At what percent of interest rate per annum had Sunil deposited the amount?[1]
  2. After 3 years, how much total money does Sunil get with principal and interest? Calculate it.[1]
  3. If Sunil decides to distribute RS 300,000 to his brothers Chandan and Ram in the ratio 2:3, then compare the amount received by Chandan and Ram.[2]
1. Interest rate in percentage:
   Since the interest for Rs 100 in 1 year is Rs 12, the rate is 12%.
   So, Rate (R) = 12% p.a.
2. Total money after 3 years (Amount):
   Principal (P) = Rs 300,000
   Time (T) = 3 years
   Rate (R) = 12%
   Interest (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{300,000 \times 3 \times 12}{100} = 108,000 \)
   Total Amount (A) = P + I = 300,000 + 108,000 = 408,000
   So, Sunil gets a total of Rs 408,000.
3. Comparison of amount received by Chandan and Ram:
   Total Amount = Rs 300,000
   Ratio (Chandan : Ram) = 2 : 3
   Sum of ratios = 2 + 3 = 5
   Chandan's share = \( \dfrac{2}{5} \times 300,000 = 120,000 \)
   Ram's share = \( \dfrac{3}{5} \times 300,000 = 180,000 \)
   Comparison: Ram receives Rs 60,000 (180,000 - 120,000) more than Chandan.
• सुनीलले राष्ट्रिय वाणिज्य बैंकमा रु. 100 को वार्षिक रु. 12 ब्याज पाउने गरी रु. 3,00,000 तीन वर्षका लागि जम्मा गरे भने:
  1. सुनीलले वार्षिक कति प्रतिशत ब्याजदरमा उक्त रकम जम्मा गरेका थिए ? [1]
  2. 3 वर्षपछि सुनीलले साँवा र ब्याजसहित जम्मा कति रकम (मिश्रधन) प्राप्त गर्छन् ? गणना गर्नुहोस् । [1]
  3. यदि सुनीलले रु. 3,00,000 आफ्ना भाइहरू चन्दन र रामलाई 2:3 को अनुपातमा बाँड्ने निर्णय गरे भने, चन्दन र रामले प्राप्त गर्ने रकम बीच तुलना गर्नुहोस् । [2]
1. ब्याजदर प्रतिशतमा:
   रु. 100 को 1 वर्षको ब्याज रु. 12 हुनु भनेको ब्याजदर 12% हुनु हो ।
   तसर्थ, ब्याजदर (R) = 12% प्रति वर्ष ।
2. 3 वर्षपछिको जम्मा रकम (मिश्रधन):
   साँवा (P) = रु. 3,00,000
   समय (T) = 3 वर्ष
   दर (R) = 12%
   ब्याज (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{3,00,000 \times 3 \times 12}{100} = 1,08,000 \)
   जम्मा रकम (A) = P + I = 3,00,000 + 1,08,000 = 4,08,000
   तसर्थ, उनले जम्मा रु. 4,08,000 प्राप्त गर्नेछन् ।
3. चन्दन र रामले पाउने रकमको तुलना:
   जम्मा रकम = रु. 3,00,000
   अनुपात (चन्दन : राम) = 2 : 3
   अनुपातको योग = 2 + 3 = 5
   चन्दनले पाउने रकम = \( \dfrac{2}{5} \times 3,00,000 = 1,20,000 \)
   रामले पाउने रकम = \( \dfrac{3}{5} \times 3,00,000 = 1,80,000 \)
   तुलना: रामले चन्दनको तुलनामा रु. 60,000 (1,80,000 - 1,20,000) बढी रकम प्राप्त गर्छन् ।

Question 28

• Dilliram deposited Rs 120,000 in a bank at the rate of 12% per annum.
  1. Write a formula to calculate simple interest.[1]
  2. How much interest does Dilliram get after 6 years?[1]
  3. If he has to pay 5% of interest as income tax, how much amount will he receive after 6 years?[2]
1. Formula for Simple Interest:
   Simple Interest (I) = \( \dfrac{P \times T \times R}{100} \)
2. Interest after 6 years:
   Principal (P) = Rs. 120,000
   Time (T) = 6 years
   Rate (R) = 12%
   Thus,
   Interest (I) = \( \dfrac{120,000 \times 6 \times 12}{100} = 86,400 \)
   So, he gets Rs. 86,400 as interest.
3. Total amount after tax deduction:
   Total Interest = Rs. 86,400
   Income Tax (5%) = \( \dfrac{5}{100} \times 86,400 = 4,320 \)
   Net Interest = 86,400 - 4,320 = Rs. 82,080
   Total Amount Received (A) = Principal + Net Interest = 120,000 + 82,080 = 202,080
   So, he will receive a total of Rs. 202,080.
• डिल्लीरामले वार्षिक 12% ब्याजदरमा एउटा बैंकमा रु. 1,20,000 जम्मा गरे भने:
  1. साधारण ब्याज गणना गर्ने सूत्र लेख्नुहोस् । [1]
  2. 6 वर्षपछि डिल्लीरामले कति ब्याज प्राप्त गर्छन् ? [1]
  3. यदि उनले ब्याजको 5% रकम आयकर (Income Tax) तिर्नुपर्छ भने, 6 वर्षपछि उनले जम्मा कति रकम प्राप्त गर्नेछन् ? [2]
1. साधारण ब्याजको सूत्र:
   साधारण ब्याज (I) = \( \dfrac{P \times T \times R}{100} \)
2. 6 वर्षको ब्याज:
   साँवा (P) = रु. 1,20,000
   समय (T) = 6 वर्ष
   दर (R) = 12%
   यसरी,
   ब्याज (I) = \( \dfrac{1,20,000 \times 6 \times 12}{100} = 86,400 \)
   तसर्थ, उनले रु. 86,400 ब्याज प्राप्त गर्छन् ।
3. कर कटाएर प्राप्त हुने जम्मा रकम:
   जम्मा ब्याज = रु. 86,400
   आयकर (5%) = \( \dfrac{5}{100} \times 86,400 = 4,320 \)
   खुद ब्याज (Net Interest) = 86,400 - 4,320 = रु. 82,080
   जम्मा प्राप्त हुने रकम (A) = साँवा + खुद ब्याज = 1,20,000 + 82,080 = 2,02,080
   तसर्थ, उनले जम्मा रु. 2,02,080 प्राप्त गर्नेछन् ।

Question 29

• Two friends, Ramnaresh and Mahesh, invested Rs. 50,00,000 in a factory in the ratio of 3:2.
  1. What is the difference between direct and indirect variation? Write one difference. [1]
  2. How much amount has Ramnaresh invested in the factory? Find it. [1]
  3. If Mahesh had deposited the amount invested in the industry in a bank at an annual interest rate of 10%, how much simple interest would he have received after 2 years? Calculate. [2]
  4. If 3 : 2 = x : 500, find the value of x. [1]
1. Difference in Variation:
   In direct variation, as one quantity increases, the other also increases; however, in indirect variation, as one quantity increases, the other decreases.
2. Investment of Ramnaresh:
   Total Investment = Rs. 50,00,000
   Ratio = 3:2 (Ramnaresh : Mahesh)
   Sum of ratios = 3 + 2 = 5
   Thus,
   Ramnaresh's Investment = \( \dfrac{3}{5} \times 50,00,000 = 30,00,000 \)
   So, Ramnaresh invested Rs. 30,00,000.
3. Interest Calculation for Mahesh:
   Mahesh's Investment (P) = \( \dfrac{2}{5} \times 50,00,000 = Rs. 20,00,000 \)
   Rate (R) = 10%
   Time (T) = 2 years
   Thus,
   Simple Interest (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{20,00,000 \times 2 \times 10}{100} = 4,00,000 \)
   So, he would have received Rs. 4,00,000 as simple interest.
4. Value of x:
   Given: \( 3 : 2 = x : 500 \)
   Or, \( \dfrac{3}{2} = \dfrac{x}{500} \)
   Or, \( 2x = 1500 \)
   Or, \( x = 750 \)
   So, the value of x is 750.
• दुई जना साथी रामनरेश र महेशले एउटा कारखानामा 3:2 को अनुपातमा रु. 50,00,000 लगानी गरे:
  1. प्रत्यक्ष र अप्रत्यक्ष विचरणमा के फरक छ? एउटा फरक लेख्नुहोस्। [1]
  2. रामनरेशले कारखानामा कति रकम लगानी गरेको थियो? पत्ता लगाउनुहोस्। [1]
  3. यदि महेशले उद्योगमा लगानी गरेको रकम बैंकमा 10% वार्षिक ब्याजदरमा जम्मा गरेको भए 2 वर्षपछि कति साधारण ब्याज पाउँथ्यो? गणना गर्नुहोस्। [2]
  4. यदि 3 : 2 = x : 500 भए, x को मान पत्ता लगाउनुहोस्। [1]
1. विचरणमा फरक:
   प्रत्यक्ष विचरणमा एउटा परिमाण बढ्दा अर्को पनि बढ्छ (वा घट्दा घट्छ), तर अप्रत्यक्ष विचरणमा एउटा परिमाण बढ्दा अर्को घट्छ (वा घट्दा बढ्छ) ।
2. रामनरेशको लगानी:
   जम्मा लगानी = रु. 50,00,000
   अनुपात = 3:2 (रामनरेश : महेश)
   अनुपातको योग = 3 + 2 = 5
   यसरी,
   रामनरेशको लगानी = \( \dfrac{3}{5} \times 50,00,000 = 30,00,000 \)
   तसर्थ, रामनरेशले रु. 30,00,000 लगानी गरेका थिए ।
3. महेशको ब्याज गणना:
   महेशको लगानी (P) = \( \dfrac{2}{5} \times 50,00,000 = रु. 20,00,000 \)
   ब्याजदर (R) = 10%
   समय (T) = 2 वर्ष
   यसरी,
   साधारण ब्याज (I) = \( \dfrac{P \times T \times R}{100} = \dfrac{20,00,000 \times 2 \times 10}{100} = 4,00,000 \)
   तसर्थ, उनले रु. 4,00,000 ब्याज पाउँथे ।
4. x को मान:
   हामीलाई दिइएको छ: \( 3 : 2 = x : 500 \)
   वा, \( \dfrac{3}{2} = \dfrac{x}{500} \)
   वा, \( 2x = 3 \times 500 \)
   वा, \( x = \dfrac{1500}{2} \)
   तसर्थ, x = 750 ।

Question 30

• Manju pays Rs. 2,400 at interest at the rate of 10% p.a. in 3 years.
  1. Express P in terms of I, T and R. [1K]
  2. How much loan has she taken? Calculate it. [2A]
  3. By what percent is the interest less than the principal? Find it. [1HA]
1. Expression of P in terms of I, T and R:
   Principal (P) = \( \frac{100 \times I}{R \times T} \)
2. Calculation of the loan (Principal):
   Given,
   Interest (I) = Rs. 2,400
   Time (T) = 3 years
   Rate (R) = 10%
   We know,
   \( P = \frac{100 \times 2400}{10 \times 3} = \frac{2,40,000}{30} = 8,000 \)
   So, she has taken a loan of Rs. 8,000.
3. Percentage by which interest is less than principal:
   Principal (P) = Rs. 8,000
   Interest (I) = Rs. 2,400
   Difference = P - I = 8,000 - 2,400 = 5,600
   Percentage less = \( \frac{P - I}{P} \times 100\% \)
   = \( \frac{5,600}{8,000} \times 100\% = 70\% \)
   So, the interest is 70% less than the principal.
• मन्जुले आफूले लिएको ऋणको 3 वर्षमा वार्षिक 10% ब्याजदरले रु. 2,400 ब्याज तिरेछिन् ।
  1. P लाई I, T र R को रूपमा लेख्नुहोस् । [1K]
  2. उनले कति ऋण लिएकी रहेछिन् ? गणना गर्नुहोस् । [2A]
  3. ब्याज मूलधनभन्दा कति प्रतिशतले कम छ ? पत्ता लगाउनुहोस् । [1HA]
1. P लाई I, T र R को रूपमा व्यक्त गर्दा:
   साँवा (P) = \( \frac{100 \times I}{T \times R} \)
2. ऋण (साँवा) को गणना:
   यहाँ, ब्याज (I) = रु. 2,400
   समय (T) = 3 वर्ष
   ब्याजदर (R) = 10%
   हामीलाई थाहा छ,
   \( P = \frac{100 \times 2400}{3 \times 10} = \frac{2,40,000}{30} = 8,000 \)
   तसर्थ, उनले रु. 8,000 ऋण लिएकी रहेछिन् ।
3. ब्याज र मूलधनको तुलना:
   साँवा (P) = रु. 8,000
   ब्याज (I) = रु. 2,400
   फरक = P - I = 8,000 - 2,400 = 5,600
   ब्याज कम भएको प्रतिशत = \( \frac{P - I}{P} \times 100\% \)
   = \( \frac{5,600}{8,000} \times 100\% = 70\% \)
   तसर्थ, ब्याज मूलधनभन्दा 70% ले कम छ ।

Question 31

• Rajaram deposited Rs. 20,000 in a bank at the rate of 18% p.a. simple interest for 2 years.
  1. Write the formula to find simple interest. [1K]
  2. Find the interest of the two years. [2A]
  3. If Rajaram divided the interest between his two sons in the ratio 3:2, how much would each of them get? [2HA]
1. Formula to find simple interest:
   Simple Interest (I) = \( \frac{P \times T \times R}{100} \)
2. Finding the interest for 2 years:
   Given, Principal (P) = Rs. 20,000
   Rate (R) = 18% p.a.
   Time (T) = 2 years
   We know,
   Interest (I) = \( \frac{20,000 \times 2 \times 18}{100} = 7,200 \)
   So, the interest for 2 years is Rs. 7,200.
3. Distribution between sons:
   Total Interest = Rs. 7,200
   Ratio = 3 : 2
   Sum of ratios = 3 + 2 = 5
   First son’s share = \( \frac{3}{5} \times 7,200 = 4,320 \)
   Second son’s share = \( \frac{2}{5} \times 7,200 = 2,880 \)
   Hence, the first son gets Rs. 4,320 and the second son gets Rs. 2,880.
• राजारामले रु. 20,000 दुई वर्षको लागि 18% वार्षिक साधारण ब्याजदरमा बैङ्कमा जम्मा गरेछ ।
  1. साधारण ब्याज पत्ता लगाउने सूत्र लेख्नुहोस् । [1K]
  2. 2 वर्षको ब्याज कति हुन्छ, पत्ता लगाउनुहोस् । [2A]
  3. उक्त ब्याज राजारामले आफ्ना दुई भाइ छोरालाई 3:2 को अनुपातमा बाँडिएछन् भने प्रत्येकले कति पाउँछन् ? [2HA]
1. साधारण ब्याज पत्ता लगाउने सूत्र:
   साधारण ब्याज (I) = \( \frac{P \times T \times R}{100} \)
2. 2 वर्षको ब्याज गणना:
   यहाँ, साँवा (P) = रु. 20,000
   ब्याजदर (R) = 18%
   समय (T) = 2 वर्ष
   हामीलाई थाहा छ,
   ब्याज (I) = \( \frac{20,000 \times 2 \times 18}{100} = 7,200 \)
   तसर्थ, 2 वर्षको ब्याज रु. 7,200 हुन्छ ।
3. छोराहरूका बीचको बाँडफाँड:
   जम्मा ब्याज = रु. 7,200
   बाँडफाँडको अनुपात = 3 : 2
   अनुपातको योग = 3 + 2 = 5
   जेठो छोराको अंश = \( \frac{3}{5} \times 7,200 = 4,320 \)
   कान्छो छोराको अंश = \( \frac{2}{5} \times 7,200 = 2,880 \)
   तसर्थ, जेठो छोराले रु. 4,320 र कान्छो छोराले रु. 2,880 पाउँछन् ।

Question 32

• The simple interest on Rs. 7,200 for five years is Rs. 1,080.
  1. What is called the difference of amount and the principal? Write it.[1K]
  2. Find the rate of interest.[2A]
  3. Divide the interest into two parts in the ratio 7:5.[2HA]
1. Difference of amount and principal:
   The difference between the amount and the principal is called Simple Interest.
2. Finding the rate of interest:
   Given, Principal (P) = Rs. 7,200
   Time (T) = 5 years
   Simple Interest (I) = Rs. 1,080
   We know,
   Rate (R) = \( \frac{I \times 100}{P \times T} = \frac{1,080 \times 100}{7,200 \times 5} \)
   R = \( \frac{1,08,000}{36,000} = 3\% \)
   Therefore, the rate of interest is 3% per annum.
3. Dividing the interest (Ratio 7:5):
   Total Interest = Rs. 1,080
   Sum of ratio parts = 7 + 5 = 12
   First part = \( \frac{7}{12} \times 1,080 = 630 \)
   Second part = \( \frac{5}{12} \times 1,080 = 450 \)
   Hence, the two parts are Rs. 630 and Rs. 450.
• पाँच वर्षमा रु. 7,200 को साधारण ब्याज रु. 1,080 हुन्छ ।
  1. मिश्रधन र मूलधनको अन्तरलाई के भनिन्छ ? लेख्नुहोस् । [1K]
  2. ब्याजदर पत्ता लगाउनुहोस् । [2A]
  3. ब्याजलाई 7:5 को अनुपात हुने गरी दुई भागमा विभाजन गर्नुहोस् । [2HA]
1. मिश्रधन र मूलधनको अन्तर:
   मिश्रधन र मूलधनको अन्तरलाई साधारण ब्याज भनिन्छ ।
2. ब्याजदर गणना:
   यहाँ, साँवा (P) = रु. 7,200
   समय (T) = 5 वर्ष
   ब्याज (I) = रु. 1,080
   हामीलाई थाहा छ,
   दर (R) = \( \frac{I \times 100}{P \times T} = \frac{1,080 \times 100}{7,200 \times 5} \)
   R = \( \frac{1,08,000}{36,000} = 3\% \)
   तसर्थ, वार्षिक ब्याजदर 3% हुन्छ ।
3. ब्याजको विभाजन (अनुपात 7:5):
   जम्मा ब्याज = रु. 1,080
   अनुपातको योग = 7 + 5 = 12
   पहिलो भाग = \( \frac{7}{12} \times 1,080 = 630 \)
   दोस्रो भाग = \( \frac{5}{12} \times 1,080 = 450 \)
   तसर्थ, दुई भागहरू क्रमशः रु. 630 र रु. 450 हुन् ।

Question 33

• Sujata has deposited Rs. 45,000 in a bank at the rate of Rs. 4 interest per annum on Rs. 100.
  1. What is the rate of interest per annum?[1K]
  2. In how many years the interest of the sum becomes Rs. 9,000? Calculate it.[2A]
  3. Find the ratio of amount and interest.[2HA]
1. Rate of interest per annum:
   Since the interest is Rs. 4 on Rs. 100 per year,
   Rate (R) = 4% p.a.
2. Calculation of time:
   Given, Principal (P) = Rs. 45,000
   Rate (R) = 4% p.a.
   Interest (I) = Rs. 9,000
   We know,
   Time (T) = \( \frac{I \times 100}{P \times R} = \frac{9,000 \times 100}{45,000 \times 4} \)
   T = \( \frac{9,00,000}{1,80,000} = 5 \) years
   Therefore, it takes 5 years for the interest to become Rs. 9,000.
3. Ratio of amount and interest:
   Principal (P) = Rs. 45,000
   Interest (I) = Rs. 9,000
   Amount (A) = P + I = 45,000 + 9,000 = Rs. 54,000
   Ratio (A : I) = 54,000 : 9,000
   = \( \frac{54,000}{9,000} = \frac{6}{1} \)
   Hence, the required ratio is 6 : 1.
• सुजाताले रु. 100 को वार्षिक रु. 4 ब्याज पाउने दरले रु. 45,000 एउटा बैङ्कमा जम्मा गरिछन् ।
  1. ब्याजदर प्रतिवर्ष कति प्रतिशत रहेछ ? [1K]
  2. कति वर्षमा उक्त रकमको ब्याज रु. 9,000 हुन्छ ? गणना गर्नुहोस् । [2A]
  3. मिश्रधन र ब्याजको अनुपात पत्ता लगाउनुहोस् । [2HA]
1. ब्याजदर निर्धारण:
   रु. 100 को 1 वर्षको ब्याज रु. 4 हुनु भनेको ब्याजदर 4% हुनु हो ।
   तसर्थ, ब्याजदर (R) = 4% प्रति वर्ष ।
2. समयको गणना:
   यहाँ, साँवा (P) = रु. 45,000
   दर (R) = 4%
   ब्याज (I) = रु. 9,000
   हामीलाई थाहा छ,
   समय (T) = \( \frac{I \times 100}{P \times R} = \frac{9,000 \times 100}{45,000 \times 4} \)
   T = \( \frac{9,00,000}{1,80,000} = 5 \) वर्ष
   तसर्थ, 5 वर्षमा ब्याज रु. 9,000 हुन्छ ।
3. मिश्रधन र ब्याजको अनुपात:
   साँवा (P) = रु. 45,000
   ब्याज (I) = रु. 9,000
   मिश्रधन (A) = P + I = 45,000 + 9,000 = रु. 54,000
   अब, अनुपात (A : I) = 54,000 : 9,000
   = \( \frac{54,000}{9,000} = \frac{6}{1} \)
   तसर्थ, मिश्रधन र ब्याजको अनुपात 6 : 1 हो ।

Question 34

• Chitraman deposited Rs. 50,000 in a bank at the rate of 10% p.a. for 2 years.
  1. Write the formula to find principal.[1K]
  2. How much interest will he get in 2 years? Find it.[2A]
  3. Find the amount.[1HA]
1. Formula to find principal:
   Principal (P) = \( \frac{100 \times I}{R \times T} \)
2. Finding interest for 2 years:
   Given, Principal (P) = Rs. 50,000
   Rate (R) = 10% p.a.
   Time (T) = 2 years
   We know,
   Interest (I) = \( \frac{P \times T \times R}{100} = \frac{50,000 \times 2 \times 10}{100} = 10,000 \)
   So, he will get Rs. 10,000 as interest in 2 years.
3. Finding the amount:
   Amount (A) = Principal (P) + Interest (I)
   A = 50,000 + 10,000 = 60,000
   Hence, the amount is Rs. 60,000.
• विश्वमानले रु. 50,000 वार्षिक 10% ब्याजदरमा 2 वर्षको लागि बैङ्कमा राखेछन् ।
  1. मूलधन पत्ता लगाउने सूत्र लेख्नुहोस् । [1K]
  2. उनले 2 वर्षमा कति ब्याज पाउँछन् ? पत्ता लगाउनुहोस् । [2A]
  3. मिश्रधन पत्ता लगाउनुहोस् । [1HA]
1. मूलधन (साँवा) पत्ता लगाउने सूत्र:
   साँवा (P) = \( \frac{100 \times I}{T \times R} \)
2. 2 वर्षको ब्याज गणना:
   यहाँ, साँवा (P) = रु. 50,000
   ब्याजदर (R) = 10%
   समय (T) = 2 वर्ष
   हामीलाई थाहा छ,
   ब्याज (I) = \( \frac{P \times T \times R}{100} = \frac{50,000 \times 2 \times 10}{100} = 10,000 \)
   तसर्थ, उनले 2 वर्षमा रु. 10,000 ब्याज पाउँछन् ।
3. मिश्रधन गणना:
   मिश्रधन (A) = साँवा (P) + ब्याज (I)
   A = 50,000 + 10,000 = 60,000
   तसर्थ, मिश्रधन रु. 60,000 हो ।

Question 35

• The simple interest on Rs. 20,000 for 2 years is Rs. 7,200.
  1. Express interest rate (R) in terms of P, T and I.[1K]
  2. Find the interest rate.[2A]
  3. Divide interest into two parts in the ratio 1:2.[1HA]
1. Expression for interest rate (R):
   Expressing R in terms of P, T, and I:
   Rate (R) = \( \frac{100 \times I}{P \times T} \)
2. Finding the interest rate:
   Given, Principal (P) = Rs. 20,000
   Time (T) = 2 years
   Simple Interest (I) = Rs. 7,200
   Using the formula,
   R = \( \frac{100 \times 7,200}{20,000 \times 2} = \frac{7,20,000}{40,000} = 18 \)
   Therefore, the rate of interest is 18% per annum.
3. Dividing interest (Ratio 1:2):
   Total Interest = Rs. 7,200
   Sum of the ratio parts = 1 + 2 = 3
   First part = \( \frac{1}{3} \times 7,200 = 2,400 \)
   Second part = \( \frac{2}{3} \times 7,200 = 4,800 \)
   Hence, the two parts are Rs. 2,400 and Rs. 4,800.
• रु. 20,000 को 2 वर्षको साधारण ब्याज रु. 7,200 हुन्छ ।
  1. ब्याजदर (R) लाई P, T र I को रूपमा व्यक्त गर्नुहोस् । [1K]
  2. ब्याजदर पत्ता लगाउनुहोस् । [2A]
  3. ब्याजलाई 1:2 को अनुपातमा दुई भागमा विभाजन गर्नुहोस् । [1HA]
1. ब्याजदरको सूत्र:
   ब्याजदर (R) लाई P, T र I को रूपमा व्यक्त गर्दा:
   ब्याजदर (R) = \( \frac{100 \times I}{P \times T} \)
2. ब्याजदर गणना:
   यहाँ, साँवा (P) = रु. 20,000
   समय (T) = 2 वर्ष
   साधारण ब्याज (I) = रु. 7,200
   हामीलाई थाहा छ,
   R = \( \frac{100 \times 7,200}{20,000 \times 2} = \frac{7,20,000}{40,000} = 18\% \)
   तसर्थ, ब्याजदर वार्षिक 18% हुन्छ ।
3. ब्याजको विभाजन (अनुपात 1:2):
   जम्मा ब्याज = रु. 7,200
   अनुपातको योग = 1 + 2 = 3
   पहिलो भाग = \( \frac{1}{3} \times 7,200 = 2,400 \)
   दोस्रो भाग = \( \frac{2}{3} \times 7,200 = 4,800 \)
   तसर्थ, दुई भागहरू क्रमशः रु. 2,400 र रु. 4,800 हुन् ।

Question 36

• Hari took a loan of Rs. 3,00,000 from a bank for 2 years and 6 months at the rate of 12% p.a.
  1. In formula A = P + I, what do A, P and I represent? Write it.[1K]
  2. To clear the loan, how much amount is to be paid?[2A]
  3. Divide interest money into two parts in the ratio 4:5.[2HA]
1. Representation of Symbols:
   In the formula \( A = P + I \):
   A represents the Amount.
   P represents the Principal.
   I represents the Simple Interest.
2. Calculation of the total amount to be paid:
   Given, Principal (P) = Rs. 3,00,000
   Rate (R) = 12% p.a.
   Time (T) = 2 years 6 months = \( 2.5 \) years
   Interest (I) = \( \frac{P \times T \times R}{100} = \frac{3,00,000 \times 2.5 \times 12}{100} = 90,000 \)
   Total Amount (A) = P + I = 3,00,000 + 90,000 = 3,90,000
   Hence, Hari has to pay Rs. 3,90,000 to clear the loan.
3. Dividing interest (Ratio 4:5):
   Total interest = Rs. 90,000
   Sum of ratio parts = 4 + 5 = 9
   First part = \( \frac{4}{9} \times 90,000 = 40,000 \)
   Second part = \( \frac{5}{9} \times 90,000 = 50,000 \)
   Hence, the two parts are Rs. 40,000 and Rs. 50,000.
• हरिले एउटा बैङ्कबाट रु. 3,00,000 वार्षिक 12% ब्याजदरमा 2 वर्ष 6 महिनाका लागि ऋण लिएछ ।
  1. सूत्र A = P + I मा A, P र I ले के के जनाउँछन् ? लेख्नुहोस् । [1K]
  2. ऋण चुक्ता गर्न जम्मा कति रकम तिनुपर्छ ? [2A]
  3. ब्याज रकमलाई 4:5 को अनुपातमा दुई भागमा विभाजन गर्नुहोस् । [2HA]
1. संकेतहरूको अर्थ:
   सूत्र \( A = P + I \) मा:
   A ले मिश्रधन (Amount) जनाउँछ ।
   P ले साँवा वा मूलधन (Principal) जनाउँछ ।
   I ले साधारण ब्याज (Simple Interest) जनाउँछ ।
2. ऋण चुक्ता गर्न तिर्नुपर्ने जम्मा रकम (मिश्रधन) गणना:
   यहाँ, साँवा (P) = रु. 3,00,000
   दर (R) = 12%
   समय (T) = 2 वर्ष 6 महिना = \( 2.5 \) वर्ष
   ब्याज (I) = \( \frac{P \times T \times R}{100} = \frac{3,00,000 \times 2.5 \times 12}{100} = 90,000 \)
   जम्मा रकम (A) = P + I = 3,00,000 + 90,000 = 3,90,000
   तसर्थ, ऋण चुक्ता गर्न उनले जम्मा रु. 3,90,000 तिर्नुपर्छ ।
3. ब्याजको विभाजन (अनुपात 4:5):
   जम्मा ब्याज = रु. 90,000
   अनुपातको योग = 4 + 5 = 9
   पहिलो भाग = \( \frac{4}{9} \times 90,000 = 40,000 \)
   दोस्रो भाग = \( \frac{5}{9} \times 90,000 = 50,000 \)
   तसर्थ, दुई भागहरू क्रमशः रु. 40,000 र रु. 50,000 हुन् ।

Question 37

• Bishal Magar has deposited Rs. 35,000 in a bank at the rate of 12% p.a. for 2 years.
  1. Express amount (A) in terms of P, T and R.[1K]
  2. How much interest does Bishal get in 2 years?[2A]
  3. Find the ratio of principal and amount.[2HA]
1. Expression for amount (A):
   Expressing A in terms of P, T, and R:
   \( A = P + \frac{P \times T \times R}{100} \) or \( A = P \left( 1 + \frac{T \times R}{100} \right) \)
2. Finding interest for 2 years:
   Given, Principal (P) = Rs. 35,000
   Rate (R) = 12% p.a.
   Time (T) = 2 years
   We know,
   Interest (I) = \( \frac{35,000 \times 2 \times 12}{100} = 8,400 \)
   So, Bishal gets Rs. 8,400 as interest in 2 years.
3. Ratio of principal and amount:
   Principal (P) = Rs. 35,000
   Interest (I) = Rs. 8,400
   Amount (A) = P + I = 35,000 + 8,400 = 43,400
   Ratio (P : A) = 35,000 : 43,400
   Dividing both by 700:
   = \( \frac{350}{434} = \frac{175}{217} \)
   Hence, the ratio of principal to amount is 175 : 217.
• विशाल मगरले रु. 35,000 वार्षिक 12% ब्याजदरमा 2 वर्षका लागि एउटा बैङ्कमा जम्मा गरेछन् ।
  1. मिश्रधन (A) लाई P, T र R को रूपमा व्यक्त गर्नुहोस् । [1K]
  2. विशालले 2 वर्षमा कति ब्याज पाउँछन् ? [2A]
  3. साँवा र मिश्रधनको अनुपात पत्ता लगाउनुहोस् । [2HA]
1. मिश्रधनको सूत्र:
   मिश्रधन (A) लाई P, T र R को रूपमा व्यक्त गर्दा:
   \( A = P + \frac{P \times T \times R}{100} \) अथवा \( A = P \left( 1 + \frac{T \times R}{100} \right) \)
2. 2 वर्षको ब्याज गणना:
   यहाँ, साँवा (P) = रु. 35,000
   दर (R) = 12%
   समय (T) = 2 वर्ष
   हामीलाई थाहा छ,
   ब्याज (I) = \( \frac{35,000 \times 2 \times 12}{100} = 8,400 \)
   तसर्थ, विशालले 2 वर्षमा रु. 8,400 ब्याज पाउँछन् ।
3. साँवा र मिश्रधनको अनुपात:
   साँवा (P) = रु. 35,000
   ब्याज (I) = रु. 8,400
   मिश्रधन (A) = P + I = 35,000 + 8,400 = 43,400
   अनुपात (P : A) = 35,000 : 43,400
   दुबैलाई 700 ले भाग गर्दा:
   = \( \frac{350}{434} = \frac{175}{217} \)
   तसर्थ, साँवा र मिश्रधनको अनुपात 175 : 217 हो ।

Question 38

• A sum of money amounts to Rs. 18,900 at the rate of \(6\frac{1}{2}\%\) p.a. simple interest in 4 years.
  1. Write the formula to find simple interest. [1K]
  2. Find the sum of money. [2A]
  3. Find the ratio of amount and principal. [1HA]
1. Formula to find simple interest:
   Simple Interest (I) = \( \frac{P \times T \times R}{100} \)
2. Finding the sum of money (Principal):
   Given, Amount (A) = Rs. 18,900
   Rate (R) = \( 6\frac{1}{2}\% = 6.5\% \)
   Time (T) = 4 years
   We know, \( A = P \left(1 + \frac{TR}{100}\right) \)
   \( 18,900 = P \left(1 + \frac{4 \times 6.5}{100}\right) \)
   \( 18,900 = P \left(1 + 0.26\right) \)
   \( 18,900 = P \times 1.26 \)
   \( P = \frac{18,900}{1.26} = 15,000 \)
   Hence, the sum of money is Rs. 15,000.
3. Ratio of amount and principal:
   Amount (A) = Rs. 18,900
   Principal (P) = Rs. 15,000
   Ratio (A : P) = 18,900 : 15,000
   Dividing both by 300:
   = \( \frac{18,900}{300} : \frac{15,000}{300} = 63 : 50 \)
   Hence, the ratio of amount to principal is 63 : 50.
• कुनै धनराशिको वार्षिक \(6\frac{1}{2}\%\) साधारण ब्याजदरले 4 वर्षको मिश्रधन रु. 18,900 हुन्छ ।
  1. साधारण ब्याज निकाल्ने सूत्र लेख्नुहोस् । [1K]
  2. उक्त धनराशि कति रहेछ, पत्ता लगाउनुहोस् । [2A]
  3. मिश्रधन र मूलधनको अनुपात पत्ता लगाउनुहोस् । [1HA]
1. साधारण ब्याज निकाल्ने सूत्र:
   साधारण ब्याज (I) = \( \frac{P \times T \times R}{100} \)
2. धनराशि (साँवा) को गणना:
   यहाँ, मिश्रधन (A) = रु. 18,900
   ब्याजदर (R) = \( 6\frac{1}{2}\% = 6.5\% \)
   समय (T) = 4 वर्ष
   हामीलाई थाहा छ, \( A = P \left(1 + \frac{TR}{100}\right) \)
   \( 18,900 = P \left(1 + \frac{4 \times 6.5}{100}\right) \)
   \( 18,900 = P \left(1 + \frac{26}{100}\right) \)
   \( 18,900 = P \times 1.26 \)
   \( P = \frac{18,900}{1.26} = 15,000 \)
   तसर्थ, उक्त धनराशि रु. 15,000 हो ।
3. मिश्रधन र मूलधनको अनुपात:
   मिश्रधन (A) = रु. 18,900
   मूलधन (P) = रु. 15,000
   अनुपात (A : P) = 18,900 : 15,000
   दुवैलाई 300 ले भाग गर्दा:
   = \( \frac{18,900}{300} : \frac{15,000}{300} = 63 : 50 \)
   तसर्थ, मिश्रधन र मूलधनको अनुपात 63 : 50 हो ।

Question 39

• Harkaman took a loan of Rs. 50,000 from a commercial bank at the rate of 13% p.a. simple interest. He cleared the loan by paying Rs. 63,000.
  1. What is rate of interest, write it. [1K]
  2. How much interest did he pay? Find it. [2A]
  3. After how many years did he clear the loan? Find it. [2HA]
1. Definition of Rate of Interest:
   The rate of interest is the percentage of the principal charged as interest per year (per Rs. 100 per annum).
2. Finding the interest paid:
   Given, Principal (P) = Rs. 50,000
   Amount paid (A) = Rs. 63,000
   We know,
   Interest (I) = A - P = 63,000 - 50,000 = 13,000
   Hence, Harkaman paid Rs. 13,000 as interest.
3. Finding the time (years):
   Using the formula,
   \( T = \frac{I \times 100}{P \times R} = \frac{13,000 \times 100}{50,000 \times 13} \)
   \( T = \frac{13,00,000}{6,50,000} = 2 \) years
   Therefore, he cleared the loan after 2 years.
• हर्कमानले एउटा वाणिज्य बैङ्कबाट वार्षिक 13% साधारण ब्याजमा रु. 50,000 ऋण लिएका रहेछन् । उनले रु. 63,000 तिरेर ऋण चुक्ता गरेछन् ।
  1. ब्याजदर केलाई भनिन्छ, लेख्नुहोस् । [1K]
  2. उनले जम्मा कति ब्याज तिरेछन् ? पत्ता लगाउनुहोस् । [2A]
  3. उनले कति वर्षपछि ऋण चुक्ता गरेछन् ? पत्ता लगाउनुहोस् । [2HA]
1. ब्याजदरको परिभाषा:
   प्रतिवर्ष प्रति रु. १०० साँवामा लाग्ने ब्याजलाई ब्याजदर भनिन्छ । यसलाई सामान्यतया प्रतिशतमा व्यक्त गरिन्छ ।
2. ब्याज रकमको गणना:
   यहाँ, साँवा (P) = रु. 50,000
   मिश्रधन (A) = रु. 63,000
   हामीलाई थाहा छ,
   ब्याज (I) = A - P = 63,000 - 50,000 = 13,000
   तसर्थ, उनले जम्मा रु. 13,000 ब्याज तिरेछन् ।
3. समयको गणना:
   यहाँ, ब्याज (I) = रु. 13,000, साँवा (P) = रु. 50,000, दर (R) = 13%
   हामीलाई थाहा छ,
   समय (T) = \( \frac{I \times 100}{P \times R} = \frac{13,000 \times 100}{50,000 \times 13} \)
   T = \( \frac{13,00,000}{6,50,000} = 2 \) वर्ष
   तसर्थ, उनले 2 वर्ष पछि ऋण चुक्ता गरेछन् ।

Question 40

• Manoj pays a simple interest of Rs. 24,000 for the loan taken for 3 years at the rate of 10% p.a.
  1. In simple interest, what is the relation of A, P and I? Write it. [1K]
  2. How much loan had he taken? [2A]
  3. How much did he pay to clear the loan? [1HA]
1. Relation between A, P, and I:
   Amount (A) = Principal (P) + Interest (I)
2. Calculation of the loan (Principal):
   Given, Interest (I) = Rs. 24,000
   Time (T) = 3 years
   Rate (R) = 10% p.a.
   We know,
   Principal (P) = \( \frac{I \times 100}{T \times R} = \frac{24,000 \times 100}{3 \times 10} = 80,000 \)
   So, he had taken a loan of Rs. 80,000.
3. Total amount paid to clear the loan:
   Amount (A) = Principal (P) + Interest (I)
   A = 80,000 + 24,000 = 1,04,000
   Hence, he paid Rs. 1,04,000 to clear the loan.
• मनोजले 10% वार्षिक साधारण ब्याजमा 3 वर्षको लागि लिएको ऋणमा रु. 24,000 ब्याज तिर्छन् ।
  1. साधारण ब्याजमा A, P र I को सम्बन्ध कस्तो हुन्छ ? लेख्नुहोस् । [1K]
  2. उनले जम्मा कति रकम ऋण लिएका रहेछन् ? [2A]
  3. उनले जम्मा कति रकम तिरी ऋण चुक्ता गरेछन् ? [1HA]
1. A, P र I बिचको सम्बन्ध:
   मिश्रधन (A) = साँवा (P) + ब्याज (I)
2. ऋण (साँवा) को गणना:
   यहाँ, ब्याज (I) = रु. 24,000
   समय (T) = 3 वर्ष
   दर (R) = 10%
   हामीलाई थाहा छ,
   साँवा (P) = \( \frac{I \times 100}{T \times R} = \frac{24,000 \times 100}{3 \times 10} = 80,000 \)
   तसर्थ, उनले रु. 80,000 ऋण लिएका रहेछन् ।
3. ऋण चुक्ता गर्न तिरेको जम्मा रकम (मिश्रधन):
   हामीलाई थाहा छ,
   मिश्रधन (A) = P + I = 80,000 + 24,000 = 1,04,000
   तसर्थ, उनले रु. 1,04,000 तिरी ऋण चुक्ता गरेछन् ।

Question 41

• The amount of a sum kept in a bank at 5% p.a. for 4 years and 6 months is Rs. 251223.
  1. Write the formula to find the principal (P) when amount (A), rate (R) and time (T) are given. [1K]
  2. Find the principal. [2A]
  3. Find interest. [1U]
1. Formula to find principal (P):
   Principal (P) = \( \frac{A \times 100}{100 + T \times R} \)
2. Finding the principal:
   Given, Amount (A) = Rs. 251,223
   Rate (R) = 5% p.a.
   Time (T) = 4 years 6 months = 4.5 years
   We know,
   P = \( \frac{251,223 \times 100}{100 + 4.5 \times 5} = \frac{25,122,300}{122.5} = 205,080 \)
   Hence, the principal is Rs. 2,05,080.
3. Finding the interest:
   Interest (I) = Amount (A) – Principal (P)
   I = 251,223 – 205,080 = 46,143
   So, the interest is Rs. 46,143.
• केही रकम एउटा बैङ्कमा 5% वार्षिक ब्याजमा 4 वर्ष 6 महिनाका लागि जम्मा गर्दा मिश्रधन रु. 251223 हुन्छ ।
  1. मिश्रधन (A), ब्याजदर (R) र समय (T) दिइएको अवस्थामा मूलधन (P) पत्ता लगाउने सूत्र लेख्नुहोस् । [1K]
  2. मूलधन पत्ता लगाउनुहोस् । [2A]
  3. ब्याज रकम पत्ता लगाउनुहोस् । [1U]
1. मूलधन पत्ता लगाउने सूत्र:
   मूलधन (P) = \( \frac{A \times 100}{100 + T \times R} \)
2. मूलधनको गणना:
   यहाँ, मिश्रधन (A) = रु. 2,51,223
   ब्याजदर (R) = 5%
   समय (T) = 4 वर्ष 6 महिना = 4.5 वर्ष
   हामीलाई थाहा छ,
   P = \( \frac{2,51,223 \times 100}{100 + 4.5 \times 5} = \frac{2,51,22,300}{122.5} = 2,05,080 \)
   तसर्थ, मूलधन रु. 2,05,080 हो ।
3. ब्याज रकमको गणना:
   हामीलाई थाहा छ,
   ब्याज (I) = मिश्रधन (A) – मूलधन (P)
   I = 2,51,223 – 2,05,080 = 46,143
   तसर्थ, ब्याज रकम रु. 46,143 हो ।

Question 42

• Eliza took a loan of Rs. 80,000 from Nabil bank for 4 years at the rate of 10% p.a. simple interest.
  1. Write amount (A) in terms of P and I. [1K]
  2. How much interest should she pay in 4 years? Calculate it. [2A]
  3. Find the ratio of principal and amount. [2HA]
1. Amount in terms of P and I:
   Amount (A) = Principal (P) + Interest (I)
2. Calculation of interest for 4 years:
   Given, Principal (P) = Rs. 80,000
   Rate (R) = 10% p.a.
   Time (T) = 4 years
   We know,
   Interest (I) = \( \frac{P \times T \times R}{100} = \frac{80,000 \times 4 \times 10}{100} = 32,000 \)
   So, she should pay Rs. 32,000 as interest.
3. Ratio of principal and amount:
   Principal (P) = Rs. 80,000
   Amount (A) = P + I = 80,000 + 32,000 = 1,12,000
   Ratio (P : A) = 80,000 : 1,12,000
   = \( \frac{80}{112} = \frac{5}{7} \)
   Hence, the ratio of principal to amount is 5 : 7.
• एलिजाले नबिल बैङ्कबाट 10% प्रतिवर्ष साधारण ब्याजमा 4 वर्षका लागि रु. 80,000 ऋण लिइन् ।
  1. मिश्रधन (A) लाई P र I को रूपमा लेख्नुहोस् । [1K]
  2. उनले 4 वर्षमा जम्मा कति ब्याज तिनुपर्छ ? गणना गर्नुहोस् । [2A]
  3. मूलधन र मिश्रधनको अनुपात पत्ता लगाउनुहोस् । [2HA]
1. मिश्रधनको सम्बन्ध:
   मिश्रधन (A) = साँवा (P) + ब्याज (I)
2. 4 वर्षको ब्याज गणना:
   यहाँ, साँवा (P) = रु. 80,000
   दर (R) = 10%
   समय (T) = 4 वर्ष
   हामीलाई थाहा छ,
   ब्याज (I) = \( \frac{P \times T \times R}{100} = \frac{80,000 \times 4 \times 10}{100} = 32,000 \)
   तसर्थ, उनले 4 वर्षमा रु. 32,000 ब्याज तिनुपर्छ ।
3. साँवा र मिश्रधनको अनुपात:
   साँवा (P) = रु. 80,000
   मिश्रधन (A) = P + I = 80,000 + 32,000 = 1,12,000
   अनुपात (P : A) = 80,000 : 1,12,000
   = \( \frac{80}{112} = \frac{5}{7} \)
   तसर्थ, मूलधन र मिश्रधनको अनुपात 5 : 7 हो ।

Question 43

• Sumit got an amount of Rs. 15,17,000 from Everest bank at the rate of 12% p.a. for 5 years and 4 months on the sum that he deposited.
  1. Write the formula to find the principal P, when A, T and R are given. [1K]
  2. How much money did Sumit deposit in the bank? Find it. [2A]
  3. Find the ratio of interest and principal. [2HA]
1. Formula to find principal (P):
   Principal (P) = \( \frac{A \times 100}{100 + T \times R} \)
2. Finding the principal (deposited money):
   Given, Amount (A) = Rs. 15,17,000
   Rate (R) = 12% p.a.
   Time (T) = 5 years 4 months = \( 5 + \frac{4}{12} = 5 + \frac{1}{3} = \frac{16}{3} \) years
   We know,
   P = \( \frac{15,17,000 \times 100}{100 + \frac{16}{3} \times 12} = \frac{151,700,000}{164} = 925,000 \)
   Hence, Sumit deposited Rs. 9,25,000 in the bank.
3. Ratio of interest and principal:
   Principal (P) = Rs. 9,25,000
   Interest (I) = A - P = 15,17,000 - 9,25,000 = Rs. 5,92,000
   Ratio (I : P) = 592,000 : 925,000
   = \( \frac{592}{925} = \frac{16}{25} \)
   So, the ratio of interest and principal is 16 : 25.
• सुमितले एभरेस्ट बैङ्कमा आफूले जम्मा गरेको रकममा 12% ब्याजका दरले 5 वर्ष 4 महिनामा एकमुष्ट रकम रु. 15,17,000 पाएछ ।
  1. A, T र R दिइएको अवस्थामा मूलधन P पत्ता लगाउने सूत्र लेख्नुहोस् । [1K]
  2. सुमितले बैङ्कमा कति रकम जम्मा गरेको रहेछ ? पत्ता लगाउनुहोस् । [2A]
  3. ब्याज र मूलधनको अनुपात पत्ता लगाउनुहोस् । [2HA]
1. मूलधन पत्ता लगाउने सूत्र:
   मूलधन (P) = \( \frac{A \times 100}{100 + T \times R} \)
2. मूलधनको गणना:
   यहाँ, मिश्रधन (A) = रु. 15,17,000
   ब्याजदर (R) = 12%
   समय (T) = 5 वर्ष 4 महिना = \( 5 + \frac{4}{12} = 5 + \frac{1}{3} = \frac{16}{3} \) वर्ष
   हामीलाई थाहा छ,
   P = \( \frac{15,17,000 \times 100}{100 + \frac{16}{3} \times 12} = \frac{15,17,00,000}{100 + 64} = \frac{15,17,00,000}{164} = 9,25,000 \)
   तसर्थ, सुमितले बैङ्कमा रु. 9,25,000 जम्मा गरेका रहेछन् ।
3. ब्याज र मूलधनको अनुपात:
   मूलधन (P) = रु. 9,25,000
   ब्याज (I) = A - P = 15,17,000 - 9,25,000 = रु. 5,92,000
   अब, अनुपात (I : P) = 5,92,000 : 9,25,000
   = \( \frac{592}{925} = \frac{16}{25} \)
   तसर्थ, ब्याज र मूलधनको अनुपात 16 : 25 हो ।

Question 44

• The simple interest on Rs. 2,160 for 4 years is Rs. 648.
  1. What is the rate of interest? Write it. [1K]
  2. Find the rate of interest. [2A]
  3. At the same rate, how much will be the interest on Rs. 20,000 for 5 years? [2HA]
1. Definition of rate of interest:
   The rate of interest is the percentage of the principal charged as interest per year.
2. Finding the rate of interest:
   Given, Principal (P) = Rs. 2,160
   Time (T) = 4 years
   Interest (I) = Rs. 648
   We know,
   Rate (R) = \( \frac{I \times 100}{P \times T} = \frac{648 \times 100}{2,160 \times 4} \)
   R = \( \frac{64,800}{8,640} = 7.5\% \)
   Therefore, the rate of interest is 7.5% per annum.
3. Finding the new interest:
   Now, Principal (P) = Rs. 20,000
   Rate (R) = 7.5% p.a.
   Time (T) = 5 years
   We know,
   Interest (I) = \( \frac{P \times T \times R}{100} = \frac{20,000 \times 5 \times 7.5}{100} = 7,500 \)
   So, the interest will be Rs. 7,500.
• रु. 2,160 को 4 वर्षको साधारण ब्याज रु. 648 हुन्छ ।
  1. ब्याजदर केलाई भनिन्छ ? लेख्नुहोस् । [1K]
  2. ब्याजदर पत्ता लगाउनुहोस् । [2A]
  3. त्यही ब्याजदरमा रु. 20,000 को 5 वर्षको ब्याज कति हुन्छ ? [2HA]
1. ब्याजदरको परिभाषा:
   प्रतिवर्ष प्रति रु. १०० साँवामा लाग्ने ब्याजलाई ब्याजदर भनिन्छ ।
2. ब्याजदरको गणना:
   यहाँ, साँवा (P) = रु. 2,160
   समय (T) = 4 वर्ष
   ब्याज (I) = रु. 648
   हामीलाई थाहा छ,
   ब्याजदर (R) = \( \frac{I \times 100}{P \times T} = \frac{648 \times 100}{2,160 \times 4} \)
   R = \( \frac{64,800}{8,640} = 7.5\% \)
   तसर्थ, ब्याजदर 7.5% हुन्छ ।
3. नयाँ ब्याजको गणना:
   यहाँ, साँवा (P) = रु. 20,000
   ब्याजदर (R) = 7.5%
   समय (T) = 5 वर्ष
   हामीलाई थाहा छ,
   ब्याज (I) = \( \frac{P \times T \times R}{100} = \frac{20,000 \times 5 \times 7.5}{100} = 7,500 \)
   तसर्थ, ब्याज रु. 7,500 हुन्छ ।

Question 45

• A man took a loan of Rs. 37,500 at the rate of 7.5% p.a. simple interest.
  1. Write interest (I) in terms of P, T, and R. [1K]
  2. How much interest should he pay in 73 days? [2A]
  3. To clear the loan in one year how much amount should he pay? Calculate it. [2HA]
1. Formula for Interest:
   Expressing interest (I) in terms of P, T, and R:
   Interest (I) = \( \frac{P \times T \times R}{100} \)
2. Finding interest for 73 days:
   Given, Principal (P) = Rs. 37,500
   Rate (R) = 7.5% p.a.
   Time (T) = 73 days = \( \frac{73}{365} \) years = 0.2 years
   We know,
   Interest (I) = \( \frac{37,500 \times 0.2 \times 7.5}{100} = 562.50 \)
   So, he should pay Rs. 562.50 as interest in 73 days.
3. Calculating total amount for one year:
   Here, Time (T) = 1 year
   Interest (I) = \( \frac{P \times T \times R}{100} = \frac{37,500 \times 1 \times 7.5}{100} = 2,812.50 \)
   Total Amount (A) = Principal (P) + Interest (I) = 37,500 + 2,812.50 = 40,312.50
   Therefore, to clear the loan in one year, he should pay Rs. 40,312.50.
• एक मानिसले वार्षिक 7.5% साधारण ब्याजदरमा रु. 37,500 ऋण लिएछ ।
  1. ब्याज (I) लाई P, T र R को रूपमा लेख्नुहोस् । [1K]
  2. उक्त मानिसले 73 दिनमा जम्मा कति ब्याज तिनुपर्छ ? [2A]
  3. उक्त मानिसले एक वर्षमा ऋण चुक्ता गर्न जम्मा कति रकम तिनुपर्छ ? गणना गर्नुहोस् । [2HA]
1. ब्याजको सूत्र:
   ब्याज (I) लाई P, T र R को रूपमा व्यक्त गर्दा:
   ब्याज (I) = \( \frac{P \times T \times R}{100} \)
2. 73 दिनको ब्याज गणना:
   यहाँ, साँवा (P) = रु. 37,500
   दर (R) = 7.5%
   समय (T) = 73 दिन = \( \frac{73}{365} \) वर्ष = 0.2 वर्ष
   हामीलाई थाहा छ,
   ब्याज (I) = \( \frac{37,500 \times 0.2 \times 7.5}{100} = 562.50 \)
   तसर्थ, 73 दिनमा उनले रु. 562.50 ब्याज तिनुपर्छ ।
3. एक वर्षको मिश्रधन गणना:
   यहाँ, समय (T) = 1 वर्ष
   ब्याज (I) = \( \frac{P \times T \times R}{100} = \frac{37,500 \times 1 \times 7.5}{100} = 2,812.50 \)
   जम्मा रकम (A) = साँवा (P) + ब्याज (I) = 37,500 + 2,812.50 = 40,312.50
   तसर्थ, एक वर्षमा ऋण चुक्ता गर्न उनले जम्मा रु. 40,312.50 तिनुपर्छ ।

Question 46

• The interest on Rs. 2400 in three years is Rs. 576.
  1. Write interest rate (R) in terms of P, T and I. [1K]
  2. Find the rate of interest. [2A]
  3. Find the interest on Rs. 4200 for two years at the same rate. [2HA]
1. Expression for interest rate (R):
   Expressing R in terms of P, T, and I:
   Rate (R) = \( \frac{I \times 100}{P \times T} \)
2. Finding the rate of interest:
   Given, Principal (P) = Rs. 2,400
   Time (T) = 3 years
   Interest (I) = Rs. 576
   We know,
   Rate (R) = \( \frac{576 \times 100}{2,400 \times 3} = \frac{57,600}{7,200} = 8\% \)
   Therefore, the rate of interest is 8% per annum.
3. Finding new interest:
   Now, Principal (P) = Rs. 4,200
   Time (T) = 2 years
   Rate (R) = 8% p.a.
   We know,
   Interest (I) = \( \frac{4,200 \times 2 \times 8}{100} = 672 \)
   Hence, the interest on Rs. 4,200 for two years is Rs. 672.
• तीन वर्षमा रु. 2,400 को ब्याज रु. 576 हुन्छ ।
  1. ब्याजदर (R) लाई P, T र I को रूपमा लेख्नुहोस् । [1K]
  2. ब्याजदर पत्ता लगाउनुहोस् । [2A]
  3. त्यही दरमा रु. 4,200 को दुई वर्षको ब्याज पत्ता लगाउनुहोस् । [2HA]
1. ब्याजदरको सूत्र:
   ब्याजदर (R) लाई P, T र I को रूपमा व्यक्त गर्दा:
   ब्याजदर (R) = \( \frac{I \times 100}{P \times T} \)
2. ब्याजदरको गणना:
   यहाँ, साँवा (P) = रु. 2,400
   समय (T) = 3 वर्ष
   ब्याज (I) = रु. 576
   हामीलाई थाहा छ,
   R = \( \frac{576 \times 100}{2,400 \times 3} = \frac{57,600}{7,200} = 8\% \)
   तसर्थ, ब्याजदर वार्षिक 8% हुन्छ ।
3. नयाँ ब्याजको गणना:
   यहाँ, साँवा (P) = रु. 4,200
   समय (T) = 2 वर्ष
   ब्याजदर (R) = 8%
   हामीलाई थाहा छ,
   ब्याज (I) = \( \frac{P \times T \times R}{100} = \frac{4,200 \times 2 \times 8}{100} = 672 \)
   तसर्थ, रु. 4,200 को ब्याज रु. 672 हुन्छ ।

Question 47

• The amount on a sum of money at the rate of 10.5% p.a. in 2 years is Rs. 3,63,000.
  1. Write the principal (P) in terms of A, T and R. [1K]
  2. Find the principal. [2U]
  3. What percent of the principal is interest? [2HA]
1. Formula for Principal (P):
   Expressing Principal (P) in terms of Amount (A), Time (T), and Rate (R):
   Principal (P) = \( \frac{A \times 100}{100 + T \times R} \)
2. Finding the principal:
   Given, Amount (A) = Rs. 3,63,000
   Rate (R) = 10.5% p.a.
   Time (T) = 2 years
   We know,
   P = \( \frac{363,000 \times 100}{100 + 2 \times 10.5} = \frac{36,300,000}{121} = 300,000 \)
   Hence, the principal is Rs. 3,00,000.
3. Calculating interest as a percentage of principal:
   Interest (I) = Amount (A) - Principal (P) = 363,000 - 300,000 = Rs. 63,000
   Percentage of interest relative to principal = \( \frac{I}{P} \times 100\% \)
   = \( \frac{63,000}{300,000} \times 100\% = 21\% \)
   Therefore, the interest is 21% of the principal.
• 10.5% प्रतिवर्ष ब्याजदरले 2 वर्षमा, कुनै धनराशिको मिश्रधन रु. 3,63,000 हुन्छ ।
  1. मूलधन (P) लाई A, T र R को रूपमा लेख्नुहोस् । [1K]
  2. मूलधन पत्ता लगाउनुहोस् । [2U]
  3. ब्याज मूलधनको कति प्रतिशत रहेछ ? पत्ता लगाउनुहोस् । [2HA]
1. मूलधनको सूत्र:
   मिश्रधन (A), समय (T) र दर (R) दिइएको अवस्थामा मूलधन (P) को सूत्र:
   साँवा (P) = \( \frac{A \times 100}{100 + T \times R} \)
2. मूलधनको गणना:
   यहाँ, मिश्रधन (A) = रु. 3,63,000
   दर (R) = 10.5%
   समय (T) = 2 वर्ष
   हामीलाई थाहा छ,
   P = \( \frac{3,63,000 \times 100}{100 + 2 \times 10.5} = \frac{3,63,00,000}{121} = 3,00,000 \)
   तसर्थ, मूलधन रु. 3,00,000 हो ।
3. ब्याज प्रतिशतको गणना:
   ब्याज (I) = A - P = 3,63,000 - 3,00,000 = रु. 63,000
   साँवाको तुलनामा ब्याजको प्रतिशत = \( \frac{I}{P} \times 100\% \)
   = \( \frac{63,000}{3,00,000} \times 100\% = 21\% \)
   तसर्थ, ब्याज मूलधनको 21% रहेछ ।

Question 48

• A sum of money trebles itself in 25 years, if it is invested in simple interest.
  1. What is the relation of the amount with the principal and interest? [1K]
  2. Find the rate of interest. [2A]
  3. In how many years will the sum of money be doubled? Find it. [2HA]
1. Relation:
   Amount (A) = Principal (P) + Interest (I)
2. Finding the rate of interest:
   Let Principal = P
   As the sum trebles, Amount (A) = 3P
   Interest (I) = A - P = 3P - P = 2P
   Time (T) = 25 years
   We know, Rate (R) = \( \frac{I \times 100}{P \times T} \)
   R = \( \frac{2P \times 100}{P \times 25} = \frac{200}{25} = 8\% \)
   Therefore, the rate of interest is 8% p.a.
3. Finding the time to double the sum:
   To double the sum, Amount (A) = 2P
   Interest (I) = A - P = 2P - P = P
   Rate (R) = 8%
   We know, Time (T) = \( \frac{I \times 100}{P \times R} \)
   T = \( \frac{P \times 100}{P \times 8} = \frac{100}{8} = 12.5 \) years
   Hence, the sum of money will be doubled in 12 years 6 months.
• साधारण ब्याजमा लगानी गर्दा, कुनै धनराशि 25 वर्षमा तेब्बर हुन्छ ।
  1. मिश्रधनको मूलधन र ब्याजसँग कस्तो सम्बन्ध हुन्छ ? [1K]
  2. ब्याजदर पत्ता लगाउनुहोस् । [2A]
  3. कति वर्षमा उक्त धनराशि दोब्बर हुन्छ ? पत्ता लगाउनुहोस् । [2HA]
1. सम्बन्ध:
   मिश्रधन (A) = मूलधन (P) + ब्याज (I)
2. ब्याजदरको गणना:
   मानौँ, मूलधन = P
   प्रश्नअनुसार, 25 वर्षमा धन तेब्बर हुन्छ, त्यसैले मिश्रधन (A) = 3P
   ब्याज (I) = A - P = 3P - P = 2P
   समय (T) = 25 वर्ष
   हामीलाई थाहा छ, ब्याजदर (R) = \( \frac{I \times 100}{P \times T} \)
   R = \( \frac{2P \times 100}{P \times 25} = \frac{200}{25} = 8\% \)
   तसर्थ, ब्याजदर वार्षिक 8% हुन्छ ।
3. दोब्बर हुन लाग्ने समयको गणना:
   धन दोब्बर हुनका लागि, मिश्रधन (A) = 2P
   ब्याज (I) = A - P = 2P - P = P
   ब्याजदर (R) = 8%
   हामीलाई थाहा छ, समय (T) = \( \frac{I \times 100}{P \times R} \)
   T = \( \frac{P \times 100}{P \times 8} = \frac{100}{8} = 12.5 \) वर्ष
   तसर्थ, उक्त धनराशि 12 वर्ष 6 महिना मा दोब्बर हुन्छ ।