Question

Simple interest on a sum of money is $\frac{9}{16}$ of the sum. If the rate is $4\frac{1}{2}\%$ per annum, find the time.

Answer 1

Let the principle be $Rsx$

And the time be $t$ years

$\therefore$ Simple Interest $=\frac{Principal\times Rate\times Time}{100}$

$=\frac{x\times \frac{9}{2}\times t}{100}$

$=\frac{x\times 9\times t}{200}$

Simple interest ( given ) $=Rs.(\frac{9}{16}\times x)$

$\therefore \frac{x\times 9\times t}{200}=\frac{9}{16}x$

$\Rightarrow t=\frac{200}{16}$ years

$=12\frac{1}{2}$ years

$=12$ years $6$ months.

Hence, the answer is $12$ years $6$ months.