A sum of money lent at compound interest for 2 years at 20\% per annum would fetch ₹ 482 more, if the interest was payable half-yearly than if it was payable annually. The sum is :
(a)₹ 10,000
(b)₹ 20,000
(c)₹ 40,000
(d)₹ 50,000
Answer
Answer (as printed): B
Explanation
Let the sum be ₹ $x$. Then, C.I. when compounded half-yearly $$=\left[x \times\left(1+\frac{10}{100}\right)^{4}-x\right]=\frac{4641}{10000} x .$$ C.I. when compounded annually $$\begin{aligned} & \qquad=\left[x \times\left(1+\frac{20}{100}\right)^{2}-x\right]=\frac{11}{25} x . \\ & \therefore \frac{4641}{10000} x-\frac{11}{25} x=482 \\ & \text { or } x=\frac{482 \times 10000}{241}=20000 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.