Question

The simple interest on a certain sum is $\frac{16}{25}$ of the sum. If the rate percent per annum and the time are numerically equal, then the rate percent is

(a) $8\%$
(b) $4\%$
(c) $6\%$
(d) $12\%$

Answer 1

The correct option is (a): $8\%$

Let the sum (P) be $Rs.x.$
Then, the simple interest $\left(I\right)=Rs.\frac{16}{25}x$
Also,
Rate $\left(R\right)=R\%$
Time $\left(T\right)=R$ years ($\because$ the rate percent per annum and the time are numerically equal)
$I=\frac{P\times R\times T}{100}$

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

$\Rightarrow R=\frac{100\times \frac{16x}{25}}{x\times R}$

$\Rightarrow R\times R=\frac{64x}{x}$

$\Rightarrow R^2=8\times 8$

$\Rightarrow R=8$
Hence, the correct option is (a).