SSC Sample Paper Mock Test-14 SSC CGL Tear-II Paper-1

On what sum does the difference between the compound interest and the simple interest for 3 yr at 10% is Rs. 31?

A) Rs. 1500

B) Rs. 1200

C) Rs. 1100

D) Rs. 1000

Correct Answer: D

Solution :

Let the sum be Rs. x.

r = 10%, n = 3yr

SI \[=\frac{x\times r\times n}{100}\]

SI \[=\frac{x\times 10\times 3}{100}=\frac{3}{10}x\]

\[\text{CI}=\left[ {{\left( 1+\frac{r}{100} \right)}^{n}}-1 \right]x=\left[ {{\left( 1+\frac{10}{100} \right)}^{3}}-1 \right]x\]

\[=\left[ {{\left( \frac{11}{10} \right)}^{3}}-1 \right]x=\left( \frac{1331}{1000}-1 \right)x=\frac{331}{1000}x\]

\[=\frac{331}{1000}x-\frac{3}{10}x=31\]

\[\Rightarrow \]\[\frac{(331-300)}{1000}x=31\Rightarrow \frac{31}{1000}x=31\]

\[\Rightarrow \] \[x=1000\]

Sum = Rs. 1000