Question

A sum of money invested at simple interest becomes Rs. $306$ at the end of $5$ years. If the interest is ${\left(\frac{9}{25}\right)}^{th}$ part of the principal, what is the rate of interest per annum ?

• A. $5\frac{1}{5}\%$ p.a.
• B. $7\frac{1}{5}\%$ p.a.
• C. $9\frac{1}{5}\%$ p.a.
• D. $11\frac{1}{5}\%$ p.a.

Answer 1

The correct option is B $7\frac{1}{5}\%$ p.a.

Let the principal $=$ Rs $x$

Then, S.I. $=$ Rs. $\frac{9}{25}x$
Amount $=P+S.I.=$ $x+\frac{9}{25}=\frac{34x}{25}$
Given, $\frac{34x}{25}=306$
$\Rightarrow x=\frac{306\times 25}{34}=Rs225$

$\Rightarrow S.I.=\frac{9}{25}\times 225=$ Rs. $81$
Now, $P=$ Rs. $225,T=5$ yrs, S.I. $=$ Rs. $81,R=?$
$\therefore \frac{\text{S.I.}\times 100}{P\times T}=\frac{81\times 100}{225\times 5}=\frac{36}{5}\%$ p.a. $=7\frac{1}{5}\%$ p.a.