Question

Simple interest on a certain sum is $\frac{9}{16}$ of the sum. Find the rate percent and the time if both are numerically equal.

Answer 1

Let the sum$=x$

Then Simple interest$=\frac{9}{16}x$

Let the rate$=R\%$ and time $=R$ years.

$S.I.=\frac{PRT}{100}$

$\Rightarrow \frac{x\times R\times R}{100}=\frac{9}{16}x$

$\Rightarrow \frac{R^2}{100}=\frac{9}{16}$

$\Rightarrow R^2=\frac{900}{16}$

$\Rightarrow R=\frac{30}{4}=\frac{15}{2}=7\frac{1}{2}$

Hence Rate of interest is $7\frac{1}{2}\%$ and time is $7\frac{1}{2}$ years.