A person lent out a certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is 25 : 8. The rate of interest per annum is
(a)10\%
(b)11\%
(c)12\%
(d)$12 \frac{1}{2} \%$
Answer
Answer (as printed): D
Explanation
Let the principal be ₹ P and the rate of interest be R\% per annum. Difference of C.I. and S.I. for 2 years $$=\left[P \times\left(1+\frac{R}{100}\right)^{2}-P\right]-\left(\frac{P \times R \times 2}{100}\right)=\frac{P R^{2}}{104} .$$ Difference of C.I. and S.I. for 3 years $$\begin{aligned} & =\left[P \times\left(1+\frac{R}{100}\right)^{3}-P\right]-\left(\frac{P \times R \times 3}{100}\right) \\ & =\frac{P R^{2}}{10^{4}}\left(\frac{300+R}{100}\right) . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.