Problems on Simple Interest
Q21. On a certain sum, the simple interest at the end of 10½ years becomes 3/4 of the sum. What is the rate percent per annum ?
(a) 7 | 1 | % |
7 |
(b) 5 | 1 | % |
3 |
(c) 3 | 1 | % |
7 |
(d) 7 | 3 | % |
7 |
Answer:
(a) 7 | 1 | % |
7 |
Let the sum be Rs. x
∴ S.I = Rs. x X (3/4) = Rs. 3x/4
t = 10½ years = 21/2 years
∴ R = | S.I X 100 | = | (3x/4) X 100 | = | 3 X 25 X 2 | = | 50 | = 7 | 1 | % |
P X t | x X (21/2) | 21 | 7 | 7 |
Q22. If the annual rate of simple interest increases from 10% to 12½%, a man's annual income increases by Rs. 1250. The Principal is
(a) 5000
(b) 15000
(c) 30000
(d) 50000
Answer: (d) 50000
Let the principal be Rs. x
Now S.I2 - S.I1 = 1250
⇒ | x X 12½ X 1 | - | x X 10 X 1 | = 1250 |
100 | 100 |
⇒ x X | 25 | - | 10x | = 125000 |
2 |
⇒ | 25x - 20x | = | = 125000 |
2 |
⇒ 5x = 125000 X 2
⇒ x = 50000
Q23. Rs. 3000 amount to Rs. 3600 in 5 years at simple interest. If the interest rate were increased by 3%, it would amount to how much ?
(a) 3775
(b) 3820
(c) 4010
(d) 4050
Answer: (d) 4050
Here P = Rs. 3000
S.I = Rs. (3600 - 3000) = Rs. 600
t = 5y
Rate = | S.I X 100 | = | 600 X 100 | = 4% |
P X t | 3000 X 5 |
New Rate of Interest = 4% + 3% = 7%
S.I = | P X r X t | = | 3000 X 7 X 5 | = Rs. 1050 |
100 | 100 |
∴ Amount = Rs. 3000 + 1050 = Rs. 4050
Q24. A certain sum of money becomes three times of itself in 10 years at simple interest. In how many years does it become double of itself at the same rate ?
(a) 3 years
(b) 4 years
(c) 5 years
(d) 7 years
Answer: (c) 5 years
Let the sum be Rs. x
∴ Amount = 3x
S.I = Rs. 3x -x = Rs. 2x
t = 10y
∴ r = | S.I X 100 | = | 2x X 100 | = 20% |
P X t | x X 10 |
Now P = Rs. x, r = 20 %, A = Rs. 2x, S.I = A - P = Rs. x
t = ?
t = | x X 100 | = 5 years |
x X 20 |
Q25. If the simple interest on a certain sum of money for 18 months at 6½ % per annum exceeds the simple interest on the same sum for 8 months at 10½ % per annum by Rs. 33. The sum is
(a) Rs 260
(b) Rs 275
(c) Rs 300
(d) Rs 350
Answer: (c) Rs 300
Let the sum be Rs. x
⇒ | x X (18/12) X (13/2) | - | x X (21/2) X (8/12) | = 33 |
100 | 100 |
⇒ | 39x | - 7x | = 3300 |
4 |
⇒ | 39x - 28x | = 3300 |
4 |
⇒ 11x = 3300
⇒ x = (3300/11) = Rs. 300
Q26. Simple interest on a certain sum at a certain annual rate of interest is 25/16 of the sum. If the numbers representing rate percent and time in years be equal, then rate percent per annum is
(a) 12½ %
(b) 13¼ %
(c) 14½ %
(d) 15¾ %
Answer: (a) 12½ %
Let the sum be Rs. x
Rate = r%
time = r years
∴ S.I = Rs. | 25x |
16 |
r = 100 X | 25x | X | 1 | X | 1 |
16 | x | r |
⇒ r2 = | 2500 |
16 |
⇒ r2 = (50/4)2
⇒ r = 25/2
∴ Rate = 12½ %
Q27. The simple interest on a sum for 4 years is two-fifth of the sum. The rate percent per annum is
(a) 7 %
(b) 9 %
(c) 10 %
(d) 12 %
Answer: (c) 10 %
Let the sum be Rs. x
∴ S.I = Rs. x X | 2 | = Rs. | 2x |
5 | 5 |
Now S.I = | P x r x t |
100 |
⇒ | 2x | = | x X r X t |
5 | 100 |
⇒ r = | 2x X 100 |
5 X x X 4 |
= 10 %
Q28. Rs. 2000 is invested at 5 % per annum simple interest. If the interest is added to the principal after every 10 years, the amount will become Rs. 4000 after ?
(a) 13 | 3 | years |
7 |
(b) 16 | 2 | years |
3 |
(c) 17 | 2 | years |
3 |
(d) 19 | 5 | years |
7 |
Answer: (b) 16 | 2 | years |
3 |
S.I for 10 years = Rs. | 2000 X 5 X 10 | = Rs. 1000 |
100 |
Principal after 10 years = Rs. 2000 + 1000
= Rs. 3000
Now amount = Rs. 4000
Principal = Rs. 3000
∴ S.I = Rs. (4000 - 3000)
= Rs. 1000
r = 5%
∴ t = | S.I X 100 | = | 1000 X 100 | = 6 | 2 | years |
P X r | 3000 X 5 | 3 |
∴ Required time = (10 + 6 | 2 | ) years |
3 |
= 16 | 2 | years |
3 |
Q29. A sum of Rs. 10 is lent to be returned in 11 monthly instalments of Rs 1 each, interest being simple. The rate of interest is
(a) 8 | 3 | % |
7 |
(b) 11 | 2 | % |
5 |
(c) 19 | 2 | % |
7 |
(d) 21 | 9 | % |
11 |
Answer:
(d) 21 | 9 | % |
11 |
Rs. 10 + S.I on Rs 10 for 11 months
= Rs. 11 + S.I on Rs. 1 for (1 + 2 + 3 + ...+ 10) monthly
⇒ Rs. 10 + S.I on Rs. 1 for 110 months = Rs 11 + S.I on Rs 1 for 55 months
⇒ S.I on Rs 1 for 55 months = Rs. 1
∴ Rate = | 100 X 12 | % | = 21 | 9 | % |
1 X 55 | 11 |
Q30. X, Y, Z are three sums of money such that Y is the simple interest on X and Z in the simple interest on y for the same time and rate. Which of the following is correct ?
(a) y2 = xz
(b) y = xz
(c) x = yz
(d) z2 = xy
Answer: (a) y2 = xz
y = S.I on Rs. x = Rs | x X r X t |
100 |
z = S.I on Rs. y = Rs | y X r X t |
100 |
∴ | y | = | x |
z | y |
⇒ y2 = xz