# 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

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