Question

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. $$
• B. $$
• C. $$
• D. $$

Answer 1

Answer: (D)

$$

Answer 2

The correct option is (D): $$Let principal sum be Rs.$P$ and rate of interest=$r\%$
Difference between S.I. and C.I.
For 2 years =$\frac{ Pr^{2} }{ 100^{2} }$
For 3 years = $\frac{ Pr^{2} }{ 100^{2} } (3+\frac{r}{100})$
Ratio = \frac{ Pr^{2} }{ 100^{2} } (3+\frac{r}{100})$$:$$\frac{ Pr^{2} }{ 100^{2} } = $25:8$
$\frac{3+\frac{r}{100}}{1}$=$\frac{25}{8}$
$\frac{r}{100}=\frac{25}{8}-3$
r=$\frac{100}{8}=12\frac{1}{2}\%$