The simple interest on a certain sum of money for $3$ years at $8\%$ per annum is half the compound interest on Rs.4000 for 2 years at 10% per annum. The sum placed on the simple interest is

The correct option is A. Rs.1750

CI earned on $P=Rs.4000,R=10\%$ and $T=2$ years is,

$CI=P(1+\frac{R}{100}{)}^T-P$

$=4000(1+\frac{10}{100}{)}^2–4000$

$=4000\times \frac{11}{10}\times \frac{11}{10}-4000$

$=40\times 11\times 11-4000$

$=Rs.840$

Now, according to the question,

SI $=\frac{1}{2}\times$ CI

$\therefore$ SI = $Rs.420$

$\Rightarrow SI=\frac{PRT}{100}$ where $R=8\%$ and $T=3$ years

$\Rightarrow P=\frac{420\times 100}{3\times 8}$

$\therefore P=Rs.1750$