# 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.I_{2} - S.I_{1} = 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 |

⇒ r^{2} = |
2500 |

16 |

⇒ r^{2} = (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) y^{2} = xz

(b) y = xz

(c) x = yz

(d) z^{2} = xy

**Answer:** (a) y^{2} = 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 |

⇒ y^{2} = xz