# Problems on Simple Interest

Q11. Find S.I on Rs. 16250 at 6% p.a. for 73 days

(a) 173

(b) 195

(c) 220

(d) 237

**Answer:** (b) 195

P = Rs. 16250 r = 6% t = 73 days = 73/365 year = 1/5 year

∴ S.I = | P X r X t | = | 16250 X 6 X 1/5 |

100 | 100 |

= | 16250 X 6 X 1 | = Rs. 195 |

100 X 5 |

Find S.I on Rs. 5400 at 5 | 2 | % p.a for 6 months |

3 |

(a) 153

(b) 165

(c) 193

(d) 201

**Answer:** (a) 153

P = Rs. 5400

r = 5 | 2 | % = | 17 | % |

3 | 3 |

t = 6 months = 6/12 year = 1/2 year

S.I = | P X r X t | = | 5400 X (17/3) X (1/2) |

100 | 100 |

= 54 X | 17 | X | 1 | = 153 |

3 | 2 |

Q13. A sum when reckoned at 10% S.I amounts to Rs. 2400 in 4 years. Find the sum.

(a) 1575.75

(b) 1610.30

(c) 1612.50

(d) 1714.30

**Answer:** (d) 1714.30

Let the sum be Rs. x

∴ S.I = | x X 10 X 4 | = | 4x |

100 | 10 |

∴ Amount = Rs ( x + | 4x | ) = Rs. | 14x |

10 | 10 |

A/Q | 14x | = 2400 |

10 |

⇒ x = | 2400 X 10 | = Rs. 1714.30 |

14 |

Q14. A certain sum is invested on simple interest. If it trebles in 5 years, what is the rate of interest ?

(a) 25 %

(b) 35 %

(c) 40 %

(d) 50 %

**Answer:** (c) 40 %

Let the sum be Rs. x

∴ Amount = Rs. 3x

∴ S.I = Rs (3x -x) = Rs. 2x

Now r = | S.I X 100 | = | 2x X 100 | = 40 % |

P X t | x X 5 |

Q15. In how many years, a sum will be thrice of it at the rate of 10% per annum ?

(a) 8 years

(b) 10 years

(c) 15 years

(d) 20 years

**Answer:** (d) 20 years

Let the sum be Rs. x

∴ Amount = Rs. 3x

∴ S.I = Rs (3x -x) = Rs. 2x

Now t = | S.I X 100 | = | 2x X 100 | = 20 years |

P X r | x X 10 |

Q16. A man invests 1/2 of his capital at 6% per annum, 1/3 at 9% per annum and the remainder at 10% per annum. If his annual income is Rs. 560, the capital is

(a) 6384.15

(b) 6825.75

(c) 7219.20

(d) 7304.35

**Answer:** (d) 7304.35

Let the capital be Rs. x

A/Q, S.I_{1} + S.I_{2} + S.I_{3} = 560

⇒ | x X (½) X 6 X 1 | + | x X (1/3) X 9 X 1 | + | { x - ((x/2) + (x/3)} X 10 X 1 | = 560 |

100 | 100 | 100 |

⇒ | 3x | + | 3x | + | (x/6) X 10 | = 560 |

100 | 100 | 100 |

⇒ 3x + 3x + | 5x | = 56000 |

3 |

⇒ | 18x + 5x | = 56000 |

3 |

⇒ 23x = 56000 X 3

⇒ x = Rs. 7304.35

Q17. The sum of money that will give Rs. 1 as simple interest per day at the rate of 4% per annum is

(a) 9036

(b) 9125

(c) 9810

(d) 9985

**Answer:** (b) 9125

1 day interest = Rs 1

∴ 365 day interest = Rs 365

∴ S.I = Rs. 365

r = 4 %

Now P = | S.I X 100 | = | 365 X 100 | = Rs. 9125 |

r X t | 4 X 1 |

Q18. The difference between the interest received from two different banks on Rs. 4000 for 2 years is Rs. 20. The difference between their rates is

(a) 0.23

(b) 0.25

(c) 0.33

(d) 0.47

**Answer:** (b) 0.25

Let the rates be x% and y%

Now S.I_{1} - S.I_{2} = 20

⇒ | 4000 X x X 2 | - | 4000 X y X 2 | = 20 |

100 | 100 |

⇒ 80x - 80y = 20

⇒ 80 (x - y) = 20

⇒ x - y = 20 / 80 = 0.25

Q19. A sum of Rs. 500 amounts to Rs. 620 in 4 years. What will it amount to if the rate of interest is increased by 2% ?

(a) 590

(b) 630

(c) 660

(d) 720

**Answer:** (c) 660

P = Rs. 500

Amount = Rs. 620

∴ S.I = Rs. (620 - 500) = Rs. 120

t = 4 years

∴ r = | S.I X 100 | = | 120 X 100 | = 6 % |

P X t | 500 X 4 |

New rate = 6% + 2% = 8%

S.I = | P X r X t | = | 500 X 8 X 4 | = 160 |

100 | 100 |

∴ Required amount = Rs. (500 + 160) = Rs. 660

Q20. The simple interest at x% per annum for x years will be Rs. x on a sum of

(a) 75/x

(b) 100/x

(c) 120/x

(d) 150/x

**Answer:** (b) 100/x

Let the sum be Rs. P

P = | S.I X 100 | = | x X 100 | = Rs. | 100 |

r X t | x X x | x |