You keep Rs 10,000 in a bank at 15% a year. How much extra money do you earn in 2 years? The answer is Rs 3,000 . That extra money is called simple interest .
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Q1. What equal annual installment will discharge a debt of Rs 600, due in 5 years, at 10% simple interest?
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Answer: C
Let each installment = x, number of installments n = 5, Rate R = 10% per annum. Debt D = Rs 600 is discharged by n equal yearly installments, each earning interest until due. Formula: D = x x [n + n(n-1)R/200]. n(n-1) = 5 x 4 = 20. n(n-1)R/200 = 20 x 10/200 = 1. Bracket = n + that = 5 + 1 = 6. x = D/bracket = 600/6 = Rs 100. Check: x x bracket = 100 x 6 = Rs 600, matching the debt.
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Q2. What equal annual installment will discharge a debt of Rs 2900, due in 5 years, at 8% simple interest?
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Answer: C
Let each installment = x, number of installments n = 5, Rate R = 8% per annum. Debt D = Rs 2900 is discharged by n equal yearly installments, each earning interest until due. Formula: D = x x [n + n(n-1)R/200]. n(n-1) = 5 x 4 = 20. n(n-1)R/200 = 20 x 8/200 = 0.8. Bracket = n + that = 5 + 0.8 = 5.8. x = D/bracket = 2900/5.8 = Rs 500. Check: x x bracket = 500 x 5.8 = Rs 2900, matching the debt.
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Q3. What equal annual installment will discharge a debt of Rs 920, due in 4 years, at 10% simple interest?
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Answer: A
Let each installment = x, number of installments n = 4, Rate R = 10% per annum. Debt D = Rs 920 is discharged by n equal yearly installments, each earning interest until due. Formula: D = x x [n + n(n-1)R/200]. n(n-1) = 4 x 3 = 12. n(n-1)R/200 = 12 x 10/200 = 0.6. Bracket = n + that = 4 + 0.6 = 4.6. x = D/bracket = 920/4.6 = Rs 200. Check: x x bracket = 200 x 4.6 = Rs 920, matching the debt.
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Q4. A certain sum of money at simple interest amounts to Rs 9600 in 6 years and to Rs 13800 in 13 years. Find the sum.
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Answer: B
Let Amount A1 = Rs 9600 at Time T1 = 6 years. Let Amount A2 = Rs 13800 at Time T2 = 13 years. The gap of 7 years between them earns S.I. = A2 – A1 = 13800 – 9600 = Rs 4200. So S.I. per year = 4200/7 = Rs 600. S.I. for T1 = 6 x 600 = Rs 3600. Principal P = A1 – S.I. for T1 = 9600 – 3600 = Rs 6000. Check: P + T2 x S.I./year = 6000 + 13 x 600 = Rs 13800, matching A2 = Rs 13800.
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Q5. A certain sum of money at simple interest amounts to Rs 22800 in 2 years and to Rs 30400 in 6 years. Find the sum.
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Answer: D
Let Amount A1 = Rs 22800 at Time T1 = 2 years. Let Amount A2 = Rs 30400 at Time T2 = 6 years. The gap of 4 years between them earns S.I. = A2 – A1 = 30400 – 22800 = Rs 7600. So S.I. per year = 7600/4 = Rs 1900. S.I. for T1 = 2 x 1900 = Rs 3800. Principal P = A1 – S.I. for T1 = 22800 – 3800 = Rs 19000. Check: P + T2 x S.I./year = 19000 + 6 x 1900 = Rs 30400, matching A2 = Rs 30400.
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Q6. A certain sum of money at simple interest amounts to Rs 30625 in 5 years and to Rs 46375 in 11 years. Find the rate of interest per annum.
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Answer: B
Let Amount A1 = Rs 30625 at Time T1 = 5 years. Let Amount A2 = Rs 46375 at Time T2 = 11 years. The gap of 6 years earns S.I. = A2 – A1 = 46375 – 30625 = Rs 15750. So S.I. per year = 15750/6 = Rs 2625. S.I. for T1 = 5 x 2625 = Rs 13125. Principal P = A1 – S.I. for T1 = 30625 – 13125 = Rs 17500. Rate R = (100 x S.I. per year)/P = (100 x 2625)/17500 = 15%. Check: (P x R x T1)/100 = (17500 x 15 x 5)/100 = Rs 13125, matching S.I. for T1.
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Q7. A certain sum of money at simple interest amounts to Rs 22230 in 2 years and to Rs 33150 in 10 years. Find the sum.
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Answer: D
Let Amount A1 = Rs 22230 at Time T1 = 2 years. Let Amount A2 = Rs 33150 at Time T2 = 10 years. The gap of 8 years between them earns S.I. = A2 – A1 = 33150 – 22230 = Rs 10920. So S.I. per year = 10920/8 = Rs 1365. S.I. for T1 = 2 x 1365 = Rs 2730. Principal P = A1 – S.I. for T1 = 22230 – 2730 = Rs 19500. Check: P + T2 x S.I./year = 19500 + 10 x 1365 = Rs 33150, matching A2 = Rs 33150.
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Q8. A certain sum of money at simple interest amounts to Rs 20520 in 2 years and to Rs 28080 in 8 years. Find the rate of interest per annum.
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Answer: C
Let Amount A1 = Rs 20520 at Time T1 = 2 years. Let Amount A2 = Rs 28080 at Time T2 = 8 years. The gap of 6 years earns S.I. = A2 – A1 = 28080 – 20520 = Rs 7560. So S.I. per year = 7560/6 = Rs 1260. S.I. for T1 = 2 x 1260 = Rs 2520. Principal P = A1 – S.I. for T1 = 20520 – 2520 = Rs 18000. Rate R = (100 x S.I. per year)/P = (100 x 1260)/18000 = 7%. Check: (P x R x T1)/100 = (18000 x 7 x 2)/100 = Rs 2520, matching S.I. for T1.
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Q9. A certain sum of money at simple interest amounts to Rs 17145 in 3 years and to Rs 20790 in 6 years. Find the rate of interest per annum.
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Answer: A
Let Amount A1 = Rs 17145 at Time T1 = 3 years. Let Amount A2 = Rs 20790 at Time T2 = 6 years. The gap of 3 years earns S.I. = A2 – A1 = 20790 – 17145 = Rs 3645. So S.I. per year = 3645/3 = Rs 1215. S.I. for T1 = 3 x 1215 = Rs 3645. Principal P = A1 – S.I. for T1 = 17145 – 3645 = Rs 13500. Rate R = (100 x S.I. per year)/P = (100 x 1215)/13500 = 9%. Check: (P x R x T1)/100 = (13500 x 9 x 3)/100 = Rs 3645, matching S.I. for T1.
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Q10. A certain sum of money at simple interest amounts to Rs 8840 in 1 year and to Rs 11220 in 8 years. Find the sum.
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Answer: B
Let Amount A1 = Rs 8840 at Time T1 = 1 year. Let Amount A2 = Rs 11220 at Time T2 = 8 years. The gap of 7 years between them earns S.I. = A2 – A1 = 11220 – 8840 = Rs 2380. So S.I. per year = 2380/7 = Rs 340. S.I. for T1 = 1 x 340 = Rs 340. Principal P = A1 – S.I. for T1 = 8840 – 340 = Rs 8500. Check: P + T2 x S.I./year = 8500 + 8 x 340 = Rs 11220, matching A2 = Rs 11220.
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Q11. A certain sum of money at simple interest amounts to Rs 13625 in 1 year and to Rs 20375 in 7 years. Find the rate of interest per annum.
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Answer: C
Let Amount A1 = Rs 13625 at Time T1 = 1 year. Let Amount A2 = Rs 20375 at Time T2 = 7 years. The gap of 6 years earns S.I. = A2 – A1 = 20375 – 13625 = Rs 6750. So S.I. per year = 6750/6 = Rs 1125. S.I. for T1 = 1 x 1125 = Rs 1125. Principal P = A1 – S.I. for T1 = 13625 – 1125 = Rs 12500. Rate R = (100 x S.I. per year)/P = (100 x 1125)/12500 = 9%. Check: (P x R x T1)/100 = (12500 x 9 x 1)/100 = Rs 1125, matching S.I. for T1.
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Q12. A certain sum of money at simple interest amounts to Rs 21700 in 4 years and to Rs 31000 in 10 years. Find the sum.
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Answer: A
Let Amount A1 = Rs 21700 at Time T1 = 4 years. Let Amount A2 = Rs 31000 at Time T2 = 10 years. The gap of 6 years between them earns S.I. = A2 – A1 = 31000 – 21700 = Rs 9300. So S.I. per year = 9300/6 = Rs 1550. S.I. for T1 = 4 x 1550 = Rs 6200. Principal P = A1 – S.I. for T1 = 21700 – 6200 = Rs 15500. Check: P + T2 x S.I./year = 15500 + 10 x 1550 = Rs 31000, matching A2 = Rs 31000.
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Q13. A certain sum of money at simple interest amounts to Rs 5200 in 3 years and to Rs 6000 in 5 years. Find the sum.
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Answer: D
Let Amount A1 = Rs 5200 at Time T1 = 3 years. Let Amount A2 = Rs 6000 at Time T2 = 5 years. The gap of 2 years between them earns S.I. = A2 – A1 = 6000 – 5200 = Rs 800. So S.I. per year = 800/2 = Rs 400. S.I. for T1 = 3 x 400 = Rs 1200. Principal P = A1 – S.I. for T1 = 5200 – 1200 = Rs 4000. Check: P + T2 x S.I./year = 4000 + 5 x 400 = Rs 6000, matching A2 = Rs 6000.
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Q14. A sum of Rs 5000 amounts to Rs 5600 in 3 years at simple interest. If the interest rate is increased by 5%, what would the sum amount to in the same period?
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Answer: A
Let Principal P = Rs 5000, Time T = 3 years. Original S.I. = Amount – Principal = 5600 – 5000 = Rs 600. Original rate R = (100 x S.I.)/(P x T) = (100 x 600)/(5000 x 3) = 4%. New rate = R + 5 = 4 + 5 = 9%. New S.I. = (P x new rate x T)/100 = (5000 x 9 x 3)/100 = Rs 1350. New amount = Principal + new S.I. = 5000 + 1350 = Rs 6350. Check: new S.I. – old S.I. = 1350 – 600 = Rs 750, from the 5% rate rise.
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Q15. A sum of Rs 4000 amounts to Rs 5440 in 3 years at simple interest. If the interest rate is increased by 1%, what would the sum amount to in the same period?
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Answer: D
Let Principal P = Rs 4000, Time T = 3 years. Original S.I. = Amount – Principal = 5440 – 4000 = Rs 1440. Original rate R = (100 x S.I.)/(P x T) = (100 x 1440)/(4000 x 3) = 12%. New rate = R + 1 = 12 + 1 = 13%. New S.I. = (P x new rate x T)/100 = (4000 x 13 x 3)/100 = Rs 1560. New amount = Principal + new S.I. = 4000 + 1560 = Rs 5560. Check: new S.I. – old S.I. = 1560 – 1440 = Rs 120, from the 1% rate rise.
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Q16. A sum of Rs 3500 amounts to Rs 5075 in 3 years at simple interest. If the interest rate is increased by 4%, what would the sum amount to in the same period?
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Answer: B
Let Principal P = Rs 3500, Time T = 3 years. Original S.I. = Amount – Principal = 5075 – 3500 = Rs 1575. Original rate R = (100 x S.I.)/(P x T) = (100 x 1575)/(3500 x 3) = 15%. New rate = R + 4 = 15 + 4 = 19%. New S.I. = (P x new rate x T)/100 = (3500 x 19 x 3)/100 = Rs 1995. New amount = Principal + new S.I. = 3500 + 1995 = Rs 5495. Check: new S.I. – old S.I. = 1995 – 1575 = Rs 420, from the 4% rate rise.
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Q17. A sum of Rs 6000 amounts to Rs 7200 in 4 years at simple interest. If the interest rate is increased by 5%, what would the sum amount to in the same period?
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Answer: C
Let Principal P = Rs 6000, Time T = 4 years. Original S.I. = Amount – Principal = 7200 – 6000 = Rs 1200. Original rate R = (100 x S.I.)/(P x T) = (100 x 1200)/(6000 x 4) = 5%. New rate = R + 5 = 5 + 5 = 10%. New S.I. = (P x new rate x T)/100 = (6000 x 10 x 4)/100 = Rs 2400. New amount = Principal + new S.I. = 6000 + 2400 = Rs 8400. Check: new S.I. – old S.I. = 2400 – 1200 = Rs 1200, from the 5% rate rise.
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Q18. A sum of Rs 4500 amounts to Rs 5400 in 2 years at simple interest. If the interest rate is increased by 4%, what would the sum amount to in the same period?
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Answer: A
Let Principal P = Rs 4500, Time T = 2 years. Original S.I. = Amount – Principal = 5400 – 4500 = Rs 900. Original rate R = (100 x S.I.)/(P x T) = (100 x 900)/(4500 x 2) = 10%. New rate = R + 4 = 10 + 4 = 14%. New S.I. = (P x new rate x T)/100 = (4500 x 14 x 2)/100 = Rs 1260. New amount = Principal + new S.I. = 4500 + 1260 = Rs 5760. Check: new S.I. – old S.I. = 1260 – 900 = Rs 360, from the 4% rate rise.
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Q19. A sum of Rs 16500 amounts to Rs 18480 in 3 years at simple interest. If the interest rate is increased by 1%, what would the sum amount to in the same period?
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Answer: B
Let Principal P = Rs 16500, Time T = 3 years. Original S.I. = Amount – Principal = 18480 – 16500 = Rs 1980. Original rate R = (100 x S.I.)/(P x T) = (100 x 1980)/(16500 x 3) = 4%. New rate = R + 1 = 4 + 1 = 5%. New S.I. = (P x new rate x T)/100 = (16500 x 5 x 3)/100 = Rs 2475. New amount = Principal + new S.I. = 16500 + 2475 = Rs 18975. Check: new S.I. – old S.I. = 2475 – 1980 = Rs 495, from the 1% rate rise.
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Q20. A sum of Rs 4000 amounts to Rs 6400 in 6 years at simple interest. If the interest rate is increased by 4%, what would the sum amount to in the same period?
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Answer: C
Let Principal P = Rs 4000, Time T = 6 years. Original S.I. = Amount – Principal = 6400 – 4000 = Rs 2400. Original rate R = (100 x S.I.)/(P x T) = (100 x 2400)/(4000 x 6) = 10%. New rate = R + 4 = 10 + 4 = 14%. New S.I. = (P x new rate x T)/100 = (4000 x 14 x 6)/100 = Rs 3360. New amount = Principal + new S.I. = 4000 + 3360 = Rs 7360. Check: new S.I. – old S.I. = 3360 – 2400 = Rs 960, from the 4% rate rise.
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Q21. A sum of Rs 10000 amounts to Rs 12100 in 3 years at simple interest. If the interest rate is increased by 4%, what would the sum amount to in the same period?
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Answer: D
Let Principal P = Rs 10000, Time T = 3 years. Original S.I. = Amount – Principal = 12100 – 10000 = Rs 2100. Original rate R = (100 x S.I.)/(P x T) = (100 x 2100)/(10000 x 3) = 7%. New rate = R + 4 = 7 + 4 = 11%. New S.I. = (P x new rate x T)/100 = (10000 x 11 x 3)/100 = Rs 3300. New amount = Principal + new S.I. = 10000 + 3300 = Rs 13300. Check: new S.I. – old S.I. = 3300 – 2100 = Rs 1200, from the 4% rate rise.
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Q22. A sum of Rs 11500 amounts to Rs 14720 in 4 years at simple interest. If the interest rate is increased by 2%, what would the sum amount to in the same period?
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Answer: B
Let Principal P = Rs 11500, Time T = 4 years. Original S.I. = Amount – Principal = 14720 – 11500 = Rs 3220. Original rate R = (100 x S.I.)/(P x T) = (100 x 3220)/(11500 x 4) = 7%. New rate = R + 2 = 7 + 2 = 9%. New S.I. = (P x new rate x T)/100 = (11500 x 9 x 4)/100 = Rs 4140. New amount = Principal + new S.I. = 11500 + 4140 = Rs 15640. Check: new S.I. – old S.I. = 4140 – 3220 = Rs 920, from the 2% rate rise.
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Q23. A sum of Rs 1000 amounts to Rs 1240 in 4 years at simple interest. If the interest rate is increased by 1%, what would the sum amount to in the same period?
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Answer: D
Let Principal P = Rs 1000, Time T = 4 years. Original S.I. = Amount – Principal = 1240 – 1000 = Rs 240. Original rate R = (100 x S.I.)/(P x T) = (100 x 240)/(1000 x 4) = 6%. New rate = R + 1 = 6 + 1 = 7%. New S.I. = (P x new rate x T)/100 = (1000 x 7 x 4)/100 = Rs 280. New amount = Principal + new S.I. = 1000 + 280 = Rs 1280. Check: new S.I. – old S.I. = 280 – 240 = Rs 40, from the 1% rate rise.
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Q24. A sum of Rs 2000 amounts to Rs 3080 in 6 years at simple interest. If the interest rate is increased by 1%, what would the sum amount to in the same period?
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Answer: C
Let Principal P = Rs 2000, Time T = 6 years. Original S.I. = Amount – Principal = 3080 – 2000 = Rs 1080. Original rate R = (100 x S.I.)/(P x T) = (100 x 1080)/(2000 x 6) = 9%. New rate = R + 1 = 9 + 1 = 10%. New S.I. = (P x new rate x T)/100 = (2000 x 10 x 6)/100 = Rs 1200. New amount = Principal + new S.I. = 2000 + 1200 = Rs 3200. Check: new S.I. – old S.I. = 1200 – 1080 = Rs 120, from the 1% rate rise.
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Q25. A sum of Rs 12500 amounts to Rs 15500 in 2 years at simple interest. If the interest rate is increased by 3%, what would the sum amount to in the same period?
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Answer: A
Let Principal P = Rs 12500, Time T = 2 years. Original S.I. = Amount – Principal = 15500 – 12500 = Rs 3000. Original rate R = (100 x S.I.)/(P x T) = (100 x 3000)/(12500 x 2) = 12%. New rate = R + 3 = 12 + 3 = 15%. New S.I. = (P x new rate x T)/100 = (12500 x 15 x 2)/100 = Rs 3750. New amount = Principal + new S.I. = 12500 + 3750 = Rs 16250. Check: new S.I. – old S.I. = 3750 – 3000 = Rs 750, from the 3% rate rise.
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