Question

A sum when reckoned at $7\frac{1}{2}\%$ per annum amounts to $Rs.3920$ in $3$ years. Find the sum.

Answer 1

Let the required sum be $Rs.x$.

$A=Rs.3920$,

$R=7\frac{1}{2}\%=\frac{15}{2}\%$,

$T=3$ years

Now,

Simple interest,(S.I).$=\frac{P\times R\times T}{100}$

$=\frac{x\times 15\times 3}{2\times 100}$

$=\frac{9x}{40}$

Now, the total amount, $A=Rs.3920$

$\Rightarrow$ A $=$ P+S.I

$\Rightarrow 3920=x+\frac{9x}{40}$

$\Rightarrow 3920=\frac{40x+9x}{40}$

$\Rightarrow 3920\times 40=49x$

$\Rightarrow \frac{3920\times 40}{49}=x$

$\Rightarrow 80\times 40=x$

$\Rightarrow 3200=x$

Hence, the required sum is $Rs.3200$.