Question

A sum of money put at $11\%$ per annum amounts to $Rs.4491$ in $2$ years $3$ months. What will it amount to in $3$ years at the same rate?

Answer 1

Given: $R=11\%$, $T=2$ years $3$ months $=2+\frac{3}{12}years=2\frac{1}{4}years=\frac{9}{4}years$

Let the required sum be $Rs.x.$

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

$=\frac{x\times 11\times \frac{9}{4}}{100}$

$=\frac{99x}{400}$

$A=P+S.I$

$=x+\frac{99x}{400}$

$=\frac{400x+99x}{400}$

$=\frac{499x}{400}$

But the amount given is $Rs.4491.$

$\Rightarrow \frac{499x}{400}=4491$

$\Rightarrow x=\frac{4491\times 400}{499}$

$\Rightarrow x=\frac{1796400}{499}$

$\therefore x=3600$

The required sum is $Rs.3600.$

For $3$ years, we have

$\therefore S.I=\frac{P\times R\times T}{100}=\frac{3600\times 11\times 3}{100}$

$=Rs.1188$

$\therefore Amount=P+S.I.=3600+1188$

$=Rs.4788$