Question

If the compound interest for $2$ years on a certain sum be Rs. $84$ and the simple interest for $3$ years on the same sum be Rs. $120$, the sum will be-

• A. Rs. $565$
• B. Rs. $450$
• C. Rs. $515$
• D. Rs. $400$

Answer 1

The correct option is D Rs. $400$

$120=\frac{P\times 3\times R}{100}$
$\Rightarrow$ $R=\frac{400}{P}$
$CI=P[{(1+\frac{R}{100})}^n-1]$
$\Rightarrow 84=P[{(1+\frac{4000}{100P})}^2-1]$
$\Rightarrow 84=P[\frac{(40+P)(40+P)}{P^2}-1]$
$\Rightarrow 84=\frac{1}{P}[1600+P^2+80P-P^2]$
$\Rightarrow 84P=1600+80P$
$\Rightarrow 4P=1600$
$\Rightarrow P=Rs.400$