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SSC MTS Model Paper 7

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Question : 89 of 99

Marks: +1, -0

The difference between compound interest (compounded annually) and simple interest on a certain sum of money at 10% per annum for 2 years is 40. The sum is :

4000
3600
4200
3200

Solution:

(a) Let the principal be x.

Compound interest

= P \left[ \left(1 + \frac{R}{100}\right)^t - 1 \right]

= x \left[ \left(1 + \frac{10}{100}\right)^2 - 1 \right]

= x \left[ (1.1)^2 - 1 \right]

= x (1.21 - 1) = 0.21 x

\text{Sl} = \frac{x \times 2 \times 10}{100} = \frac{x}{5} = 0.2 x

Acoording to the question,

0.21 x - 0.2 x = 40

= 0.01 x = 40

= x = \frac{40}{0.01} = \text{Rs}.4000

Method2:

Here, C .I.— S.l. = 540

r = 10% , T = 2 years, P = ?

\text{CI} - \text{SI} = P \left( \frac{R}{100} \right)^2

40 = P \left( \frac{10}{100} \right)^2

P = \text{Rs}.4000

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