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

Let principal sum be Rs. $$P$$ and rate of interest = $$r\%$$

Difference between S.I. and C.I. for 2 years = $$\frac{Pr^2}{100^2}$$ and for 3 years = $$\frac{Pr^2}{100^2}(3+\frac{r}{100})$$

=> Ratio = $$[\frac{Pr^2}{100^2}(3+\frac{r}{100})]:[\frac{Pr^2}{100^2}]=25:8$$

= $$\frac{3+\frac{r}{100}}{1}=\frac{25}{8}$$

=> $$\frac{r}{100}=\frac{25}{8}-3$$

=> $$\frac{r}{100}=\frac{25-24}{8}=\frac{1}{8}$$

=> $$r=\frac{100}{8}=12\frac{1}{2}\%$$

=> Ans - (D)