# Problems on Simple Interest

Q1. At which sum, the simple interest at the rate of 3¼ per annum will be Rs. 210 in 2½ years.

(a) 2311.25

(b) 2355.30

(c) 2584.60

(d) 2716.90

**Answer:** (c) 2584.60

P = ? r = 3¼ % = 13/4%; S.I = 210 t = 2½y = 5/2 y

P = | S.I X 100 |

r X t |

= | 210 X 100 | = | 210 X 100 X 8 | = Rs. 2584.60 |

(13/4) X (5/2) | 13 X 5 |

Q2. A sum of money amount to Rs. 4200 in 4 years and to Rs. 4680 in 7 years at simple interest. The rate of interest per annum is

(a) 3312

(b) 3560

(c) 3590

(d) 3626

**Answer:** (b) 3560

S.I for 3 years = Rs (4680 - 4200) = Rs. 480

∴ S.I for 1 year = Rs. (480/3) = Rs. 160

∴ S.I for 4 years = Rs. 160 X 4 = Rs. 640

Principal (P) = Rs. (4200 - 640) = Rs. 3560

∴ r = | 100 X S.I | = | 100 X 640 % | = 4.49 % |

p X t | 3560 X 4 |

Q3. How much simple interest will Rs. 3000 earn in 18 months at 5% per annum

(a) 225

(b) 250

(c) 262

(d) 310

**Answer:** (a) 225

S.I = | P X r X t | = | 3000 X (18/12) X 5 | = | 3000 X 18 X 5 | = 225 |

100 | 100 | 100 X 12 |

Q4. A man deposited Rs. 300 for 2 years, Rs. 600 for 4 years and Rs. 1200 for 6 years. He received Rs. 1020 as the simple interest. The rate of interest per annum is

(a) 10 %

(b) 15 %

(c) 20 %

(d) 30 %

**Answer:** (a) 10 %

Let the rate of interest be r %

A/Q | 300 X r X 2 | + | 600 X r X 4 | + | 1200 X r X 6 | = 1020 |

100 | 100 | 100 |

⇒ | 600r | + | 2400r | + | 7200r | = 1020 |

100 | 100 | 100 |

⇒ 600r + 2400r + 7200r = 102000

⇒ 10200r = 102000

⇒ r = 10

∴ r = 10 %

Q5. Simple interest on Rs. 600 for 4 years at 5.25% per annum is equal to the simple interest on 400 at 5% per annum for a certain period of time. The time period is ?

(a) 5 years

(b) 5.5 years

(c) 6.3 years

(d) 7.2 years

**Answer:** (c) 6.3 years

A/Q S.I for 4 years = S.I for t years

⇒ | 600 X 5.25 X 4 | = | 400 X 5 X t |

100 | 100 |

⇒ t | = | 600 X 5.25 X 4 | = | 31.5 | = 6.3 years |

400 X 5 | 5 |

Q6. A borrows Rs. 800 at the rate of 12% per annum simple interest and B borrows Rs. 910 at the rate of 10% per annum simple interest. In how many years will their amount of debts be equal ?

(a) 8 years

(b) 13 years

(c) 19 years

(d) 22 years

**Answer:** (d) 22 years

Let the required time be t years

Now 800 + | 800 X 12 X t | = 910 + | 910 X 10 X t |

100 | 100 |

⇒ 96t - 91t = 910 - 800

⇒ 5t = 110

⇒ t = 22

Q7. Rs. 5000 becomes Rs. 6200 in 4 years at a certain rate of interest. If the rate becomes 1.5 times of itself, the amount of the same principal in 5 years will be

(a) 5536

(b) 5996

(c) 6886

(d) 7250

**Answer:** (d) 7250

S.I for 4 years = Rs. (6200 - 5000) = Rs. 1200

S.I for 1 years = Rs. (1200/4) = Rs. 300

∴ Rate of Interest = | S.I X 100 | = | 1200 X 100 | = 6% |

P X t | 5000 X 4 |

Now Rate = 6 X 1.5% = 9%

∴ Required amount = 5000 + | 5000 X 9 X 5 | = Rs. (5000 + 2250) | =Rs. 7250 |

100 |

Q8. If the simple interest for 5 years be equal to 25% of the principal, it will be equal to the principal after

(a) 10 years

(b) 20 years

(c) 30 years

(d) 40 years

**Answer:** (b) 20 years

Let the principal be P and rate be r

A/Q | P X r X 5 | = P X 25% |

100 |

⇒ | p X r X 5 | = P X | 25 |

100 | 100 |

⇒ r = | 25 | X | 100 | = 5% |

100 | 5 |

Let the required time be t years

P X r X t | = P |

100 |

⇒ | P X 5 X t | = P |

100 |

⇒ t = | 100 | = 20 years |

5 |

Q9. Hari took a loan at simple interest at 6% in the first year with an increase of 0.5% in each subsequent year. He paid Rs. 3375 as interest after 4 years. How much loan did he take ?

(a) 10950

(b) 11750

(c) 12500

(d) 12700

**Answer:** (c) 12500

Now x X | 6 | X 1 + x X | 6.5 | X 1 + x X | 7 | X 1 + x X | 7.5 | X 1 = 3375 |

100 | 100 | 100 | 100 |

⇒ (6 + 6.5 + 7 + 7.5) X (x/100) = 3375

⇒ x = 3375 X (100/27) = 12500

Q10. At what rate of simple interest a certain sum will be doubled in 14 years

(a) 7 | 1 | years |

7 |

(b) 7 | 1 | years |

9 |

(c) 8 | 1 | years |

5 |

(d) 9 | 1 | years |

3 |

**Answer:**

(a) 7 | 1 | years |

7 |

Let the sum be Rs. x

Here P = Rs. x

A = Rs. 2 X x = Rs. 2x

S.I = A - P = 2x -x = Rs. x

t = 14 years

r = ?

Now r = | S.I X 100 | = | x X 100 | = | 50 | = 7 | 1 | years |

P X t | x X 14 | 7 | 7 |