Question

At simple interest a sum becomes $\frac{49}{40}$ of itself in $2\frac{1}{2}$ years. The rate of interest per annum is
(a) $7\%$
(b) $8\%$
(c) $12\%$
(d) $9\%$

Answer 1

The correct option is (d): $9\%$

Amount $=\frac{49}{40}\times$ the sum $=\frac{49}{40}P$ [$\because$ Sum $=P$]
Simple interest $\left(I\right)=$ Amount $-$ Sum $=\frac{49}{40}P-P=\frac{9}{40}P$
Let the sum $\left(P\right)$ be $x.$
Then, simple interest $\left(I\right)=\frac{9x}{40}$
Rate $\left(R\right)=R\%$
Time $\left(T\right)=2\frac{1}{2}$ years $=\frac{5}{2}$ years
$S.I=\frac{P\times R\times T}{100}$

$\Rightarrow R=\frac{100\times I}{P\times T}=\frac{100\times \frac{9x}{40}}{x\times \frac{5}{2}}=\frac{45}{5}=9\%$