Question

Simple interest on a certain sum is $\frac{4}{9}$ of the sum . Find the rate percent and time if both are numerically equal .

Answer 1

Let, principal $=P$

Rate of interest $=R$

Time $=$ Rate of interest $=R$

Interest $=\frac{4}{9}R$

Simple interest on $P=\frac{Principal\times Rate\times Time}{100}=\frac{P\times R\times R}{100}$

$\therefore \frac{P\times R^2}{100}=\frac{4}{9}P$

$\Rightarrow \frac{R^2}{100}=\frac{4}{9}$

$\Rightarrow R^2=\frac{4\times 100}{9}$

$\Rightarrow R=\frac{2\times 10}{3}$

$\Rightarrow R=\frac{20}{3}$

$\therefore$ Rate percent $=6\frac{2}{3}\%$

and time $=6\frac{2}{3}$ years.