# Simple Interest

Quantitative Aptitude Questions and Answers section on “Simple Interest” with solution and explanation for competitive examinations such as CAT, MBA, SSC, Bank PO, Bank Clerical and other examinations.
1.

A sum of money lent at simple interest amount to Rs. 880 in 2 years and to Rs. 920 in 3 years. The sum of money (in rupees) is :
[A]784
[B]800
[C]700
[D]760

800
If the principal be x and rate of interest be r % per annum then,
SI after 1 year = 920 – 880 = Rs. 40
∴ after 2 year = Rs. 80
$=> 880 = x+80$
$=> x = 880-80 = 800$
Hence option [B] is the right answer.

2.

A man took a loan from a bank at the rate of 12% per annum at simple interest. After 3 years he had to pay Rs. 5400 as interest only for the period. The principle amount borrowed by him was:
[A]2000
[B]10000
[C]15000
[D]20000

15000
Let the principal be x.
$S.I.= \frac{Principal\times Rate\times Time }{100}$
$=>5400=\frac{x\times 12\times 13}{100}$
$=>x=\frac{5400\times 100}{12\times 3}$
$=>x=Rs. 15000$
Hence option [C] is the right answer.

3.

A lends Rs. 2500 to B and certain sum to C at the same time at 7% annual simple interest. If after 4 years, A altogether receives Rs. 1120 as interest from B and C, the sum lent to C is :
[A]6500
[B]1500
[C]4000
[D]700

1500
Let the sum lent to C be x
According to the question,
$=> \frac{2500\times 7\times 4}{100}+\frac{x\times 7\times 4}{100}=1120$
$=>2500\times 28 + 28x = 112000$
$=> 2500 + x = 4000$
$=> x = 4000-2500 = 1500$
Hence option [B] is the right answer.

4.

Rs. 500 was invested at 12% per annum simple interest and a certain sum of money invested at 10% per annum simple interest. If the sum of the interest on both the sum after 4 years is Rs. 480, the latter sum of money is :
[A]550
[B]450
[C]750
[D]600

600
Simple interest gained from Rs. 500 = $\frac{500\times 12\times 4}{100}=$ $Rs. 240$
Let the other principal be x.
S.I. gained = Rs. (480 – 240) = Rs. 240
$\therefore \frac{x\times 10\times 4}{100}=$ $240$
$=>x=\frac{240\times 100}{40}=$ $600$
Hence option [D] is the right answer.

5.

At some rate of simple interest, A lent Rs. 6000 to B for 2 years and Rs. 1500 to C for 4 years and received Rs. 900 as interest from both of them together. The rate of interest per annum was:
[A]5%
[B]10%
[C]6%
[D]8%

5%
If rate of interest be R% p.a. then,
$S.I. = \frac{Principal\times Time\times Rate}{100}$
$\therefore \frac{6000\times 2\times R}{100}+\frac{1500\times 4\times R}{100}=900$
$=>120R+60R=900$
$=>180R=900$
$=>R=\frac{900}{180}=$ 5%
Hence option [A] is the right answer.

6.

What sum will amount to 7000 Rs. In 5 years at $3\frac{1}{3}\%$ simple interest?
[A]5000 Rs.
[B]6300 Rs.
[C]6000 Rs.
[D]6500 Rs.

6000 Rs.
$P = \frac{A\times 100}{100+r\times t}$
$= \frac{7000\times 100}{100+\frac{10}{3}\times 5}$
$=> \frac{7000\times 100 \times 3}{350} = 6000 Rs.$
Hence option [C] is the right answer.

7.

A sum of 1600 Rs. gives a simple interest of 252 Rs. in 2 years and 3 months. The rate of the interest per annum is :
[A]$8\%$
[B]$6\%$
[C]$7\%$
[D]$5\frac{1}{2}\%$

$7\%$
Principal = 1600 Rs.
T = 2 years 3 months
$= \left ( 2+\frac{3}{12} \right )yrs. = \left ( 2+\frac{1}{4} \right )yrs. = \frac{9}{4}yrs.$
S.I = 252 Rs.
R = % rate of interest per annum
$=> R = \frac{100\times S.I.}{P\times t}$
$= \frac{100 \times 252}{1600 \times \frac{9}{4}} = 7\%$
Rate of interest = 7% per annum
Hence option [C] is the right answer.

8.

A lent 5000 Rs. to B for 2 years and 3000 Rs. to C for 4 years on simple interest at the same rate of interest and received 2200 Rs. in all from both as interest. The rate of interest per annum is :
[A]$7\frac{1}{8}\%$
[B]10%
[C]7%
[D]5%

10%
Let the rate of the interest per annum be r%
According to the question,
$\frac{5000\times 2\times r}{100}+\frac{3000\times 4\times r}{100} = 2200$
$=> 100r +120r = 2200$
$=> 220r = 2200$
$=> r = \frac{2200}{220} = 10\%$
Hence option [B] is the right answer.

9.

What sum of money will amount to 520 Rs. in 5 years and to 568 Rs. in 7 years at simple interest?
[A]220 Rs.
[B]400 Rs.
[C]120 Rs.
[D]510 Rs.

400 Rs.
Simple interest for 2 years = (568 – 520) Rs. = 48 Rs.
∴ Interest for 5 years =
$= \frac{48}{2}\times 5 = 120 Rs.$
Principal = (520 – 120) = 400 Rs.
Hence option [B] is the right answer.

10.

A money lender finds that due to fall in the annual rate of interest $8\%$ to $7\frac{3}{4}\%$, his yearly income diminishes by 61.50 Rs. His capital is:
[A]23800 Rs.
[B]26000 Rs.
[C]22400 Rs.
[D]24600 Rs.

24600 Rs.
Difference in rate =
$\left ( 8-7\frac{3}{4} \right )\% = \frac{1}{4}\%$
Let the capital be rate x Rs.
$\therefore \frac{1}{4}\% of x = 61.50$
$=> x = 61.50\times 100\times 4$
$=> 24600 Rs.$
Hence option [D] is the right answer.