Question

The difference between the compound interest and simple interest on a certain sum at $10\%$ per annum for $2$ years is $Rs.631$. Find the sum.

• A. $Rs.54520$
• B. $Rs.72500$
• C. $Rs.63100$
• D. $Rs.42500$

Answer 1

The correct option is C $Rs.63100$

Let sum be $x$.

$\Rightarrow$ $T=2years,R=10\%$

$\Rightarrow$ $C.I.=P{(1+\frac{R}{100})}^T-P$

$\therefore$ $C.I.=x{(1+\frac{10}{100})}^2-x$

$\therefore$ $C.I.=\frac{121}{100}x-x$

$\therefore$ $C.I.=\frac{21}{100}x$

$\Rightarrow$ $S.I.=\frac{P\times R\times T}{100}$

$\Rightarrow$ $S.I.=\frac{x\times 10\times 2}{100}=\frac{x}{5}$

$\therefore$ $\frac{21}{100}x-\frac{x}{5}=631$

$\therefore$ $\frac{21-20}{100}x=631$

$\therefore$ $x=631\times 100=Rs.63100$