Problems on Simple Interest
Q31. What annual payment will discharge a debt of Rs. 630 due in 3 years at 5% per annum ?
(a) Rs. 200
(b) Rs. 220
(c) Rs. 230
(d) Rs. 235
Answer: (a) Rs. 200
Let the required annual instalment be Rs. x
Now amount of Rs. x for 2 years + Amount of Rs. x for 1 year + Rs. x = 630
⇒ (x + | x X 5 X 2 | ) + (x + | x X 5 X 1 | ) + x = 630 |
100 | 100 |
⇒ (x + | x | ) + (x + | x | ) + x = 630 |
10 | 20 |
⇒ | 11x | + | 21x | + x = 630 |
10 | 20 |
⇒ | 22x + 21x + 20x | = 630 |
20 |
⇒ 63x = 630 X 20
⇒ x = Rs. 200
Q32. A farmer borrowed Rs. 5000 at 10% per annum. At the end of 5 years he cleared his account by paying Rs. 3000 and a cow. The cost of the cow is ?
(a) Rs. 4000
(b) Rs. 4200
(c) Rs. 4500
(d) Rs. 4800
Answer: (c) Rs. 4500
P = Rs. 5000
r = 10%
t = 5y
∴ S.I = | P X r X t | = | 5000 X 10 X 5 | = Rs. 2500 |
100 | 100 |
∴ Amount = Rs. (5000 + 2500) = Rs. 7500
∴ Cost of Cow = Rs. (7500 - 3000) = Rs. 4500
Q33. A borrows Rs. 7000 at 10% per annum simple interest and B borrows Rs. 8000 at 8% per annum simple interest. In how many years will their amounts of debts be equal ?
(a) 12 2/3 years
(b) 14 2/3 years
(c) 15 2/3 years
(d) 16 2/3 years
Answer: (d) 16 2/3 years
Let, the required time be x years
Now 7000 + | 7000 X 10 X x | = 8000 + | 8000 X 8 X x |
100 | 100 |
⇒ 7000 + 700x = 8000 + 640x
⇒ 700x - 640x = 8000 - 7000
⇒ 60x = 1000
⇒ x = 1000/60 = 16 2/3 years
Q34. A man losses Rs. 45 yearly when the annual rate of interest falls from 11% to 10%. His capital is
(a) Rs 4500
(b) Rs 4650
(c) Rs 4700
(d) Rs 4750
Answer: (a) Rs 4500
Let the capital be Rs. x
Now | x X 11 X 1 | - | x X 10 X 1 | = 45 |
100 | 100 |
⇒ 11x - 10x = 4500
⇒ x = 4500
Q35. A sum of money at simple interest amounts to Rs. 2200 in 3 years and Rs. 2500 in 5 years. The sum is
(a) Rs 1600
(b) Rs 1625
(c) Rs 1750
(d) Rs 1780
Answer: (c) Rs 1750
Simple interest for 2 years = Rs. (2500 - 2200) = Rs. 300
∴ S.I for 1 year = Rs. 150
S.I for 3 years = Rs. 150 X 3 = Rs. 450
∴ The Sum = Rs. (2200 - 450) = Rs. 1750