Simple Interest problems
- 1. A man invests ? 3000 at the rate of 5% per annum. How much more should he invest at the rate of 8%, so that he can earn a total of 6% per annum?
Options- A. ? 1200
- B. ? 1300
- C. ? 1500
- D. ? 2000 Discuss
Correct Answer: ? 1500
Explanation:
Let the extra money invested = ? P
According to the question .
(3000 x 5 x 1)/100 + (P x 8 x 1)/100 = [(3000 + P) x 6 x 1)]/100
? 15000 + 8P = 18000 + 6P
? 2P = 18000 - 15000
? P = 3000/2 = ? 1500
- 2. When a bank reduce the rate of interest from 6 1/ 2% per annum to 5 1/ 2% per annum, depositor withdrew Rs. 600 and thereby his interest reduced by ? 73. Find the initial deposit.?
Options- A. ? 4000
- B. ? 6000
- C. ? 7000
- D. ? 9000 Discuss
Correct Answer: ? 4000
Explanation:
Initially ,
let P = ? A, R = 13/2% per annum and T = 1yr
SI = PRT/100 = (A x 1 x 13/2)/100 = ? 13A/200
Now, new deposit = ? (A - 600), R = 11/2 % per annum and T = 1yr
SI = PTR/100 = [(A - 600) x 1 x 11/2)/100] = ? 11(A - 600)/200
By the given condition ,
13A/200 - 11(A - 600)/200 = 73
? 13A - 11(A - 600 ) = 200 x 73
? 2A = 200 x 73 - 600 x 11
? 2A = 14600 - 6600
? 2A = 8000
? A = 4000
Hence, the initial investment is ? 4000.
- 3. A farmer borrowed ? 4200 at 10% per annum. At the end of 5 yr he cleared his account by paying ? 5000 and a cow. The cost of the cow is?
Options- A. ? 1300
- B. ? 1240
- C. ? 1200
- D. ? 1340 Discuss
Correct Answer: ? 1300
Explanation:
Amount after 5 yr, 4200 + (4200 x 10 x 5)/100
= (4200 + 2100) = Rs 6300
? Cost of the cow = (6300 - 5000) = ? 1300
- 4. The simple interest on a sum of money will be ? 600 after 10 yr. It the principle is trebled after 5 yr, what will be the total interest at the end of tenth year?
Options- A. ? 600
- B. ? 900
- C. ? 1200
- D. ? 1500 Discuss
Correct Answer: ? 1200
Explanation:
Let the principle and rate of interest be P and R%
Then, (P x R x 10)/100 = 600
? PR = 6000
Total interest at the end of year = 300 + (3P x R x 5)/100 = 300 + (15 x 6000)/100 = ? 1200
- 5. Two equal sums of money were lent at simple interest at 10% per annum for 4 yr and 5 yr, respectively. If the difference in interest for two period was ? 220, then each sum is?
Options- A. ? 880
- B. ? 1100
- C. ? 2200
- D. ? 1640 Discuss
Correct Answer: ? 2200
Explanation:
Let each sum be ? P then,
(P x 10 x 5)/100 - (P x 10 x 4)/100 = 220
? P/10 = 220
? P = 2200
Hence, each sum is ? 2200.
- 6. A man borrowed ? 12000 for 4 yr at 7 3/ 4 per annum and a year later he again borrowed another ? 12000 for 3 yr at the same rate. How much should he pay at the end to settle the loans?
Options- A. ? 30510
- B. ? 28610
- C. ? 31450
- D. ? 29590 Discuss
Correct Answer: ? 30510
Explanation:
In the first case
P = Rs. 12000, T = 4 yr and R = 31/4 % per annum
SI = PTR/100 = (12000 x 4 x 31/4)/100 = ? 3720
A = (P + SI) = (12000 + 3720) = ? 15720
In the second case
P = ? 12000, T = 3 yr and R = 31/4 % per annum
SI = PTR/100 = (12000 x 3 x 31/4)/100 = ? 2790
A = (P + SI ) = (12000 + 2790) = ? 14790
? Total memory to be paid at the end = (15720 + 14790) = ? 30510
- 7. A man took a loan at simple interest at 7% in the first year with an increase of 0.5% in each subsequent year. He pays ? 3690 as interest after 5 yr . How much loan did he take?
Options- A. ? 9250
- B. ? 9440
- C. ? 9225
- D. ? 9360 Discuss
Correct Answer: ? 9225
Explanation:
Let the loan taken be ? P Then,
[(P x 7 x 1)/100] + [(P x 7.5 x 1)/100] + [(P x 8 x 1)/100] + [(P x 8.5 x 1)/100] + [(P x 9 x 1)/100] = ? 3690
? P x (7 + 7.5 + 8 + 8.5 + 9)/100 = 3690
? (P x 40)/100 = 3690
? P = (3690 x 100)/40 = ? 9225
Hence, the loan taken was ? 9225.
- 8. What will be the difference in the compound interest on ? 50000 at 12% for one year, when the interest is paid yearly and half- yearly?
Options- A. ?. 500
- B. ? 600
- C. ? 180
- D. ? 360 Discuss
Correct Answer: ? 180
Explanation:
CI on ? 50000 at the rate of 12% for one year, when the interest is paid half-yearly
= 50000(1 + 6/100)2 - 50000
= [50000 x (53/50) x (53/50)] - 50000 = ? 6180
CI when the interest is paid yearly
= 50000(1 + 12/100)1 - 50000
= 50000(28/25 - 1) = 50000(3/25) = ? 6000
? Required difference = CI - SI = 6180 - 6000 = ? 180
- 9. Vikram borrowed ?. 6450 at 5% simple interest repayable in 4 equal instalments. What will be the annual instalment payable by him?
Options- A. ? 1710
- B. ? 1810
- C. ? 1910
- D. ? 1860 Discuss
Correct Answer: ? 1810
Explanation:
Let the annual instalment be Rs. P.
Amount of ? 100 after 4 yr = 100 + (100 x 5 x 4)/100 = ? 120
? Present Value (PV) of ? 120 due after 4 yr = ? 100
Present Value (PV) of ? due after 4 yr = 100P/120 = 5P/6
Similary, PV of ? P due after 3 yr = 20P/23
PV of ? P due after 2 yr = 10P/11
PV of ? P due after 1 yr = 20P/21
? 5P/6 + 20P/23 + 10P/11 + 20P/11 = 6450
? P = ? 1810
- 10. Subbarao was approached by two neighbour for loan. He had ? 2540, a part of which he lent to one person at 12% interest per annum and the other part was lent to the second person at 12.5%. At the end of a year, Subbarao received ? 311.60 as interest on the total loan . Calculate the amount of money of money lent by him at 12% interest .?
Options- A. ? 1360
- B. ? 1340
- C. ? 1240
- D. ? 1180 Discuss
Correct Answer: ? 1180
Explanation:
Let the amount of money lent at 12% interest be ? P.
? Amount of money lent at 12.5% interest = ? (2540 - P)
According to the question;
(P x 12 x 1)/100 + [(2540 - P) x 12.5 x 1]/100 = 311.60
? -0.5P/100 + 31750/100 = 311.60
? 0.5P = 31750 - 31160 = 590
? P = ? 1180
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