A sum of money on compound interest amounts to Rs. 10648 in 3 years and Rs. 9680 in 2 years. The rate of interest per annum is = ?

Answer: Option B

Let the sum be Rs. P and rate of interest be R% per annum. Then,
$$\begin{array}{rl}& P{\left(1+\frac{R}{100}\right)}^2=9680.....\left(1\right)\\ & P{\left(1+\frac{R}{100}\right)}^3=10648.....\left(2\right)\end{array}$$
On dividing equation (2) by (1) :
$$\begin{array}{rl}& 1+\frac{R}{100}=\frac{10648}{9680}\\ & \Rightarrow \frac{R}{100}=\frac{10648}{9680}-1\\ & \Rightarrow \frac{R}{100}=\frac{10648-9680}{9680}\\ & \Rightarrow \frac{R}{100}=\frac{968}{9680}\\ & \Rightarrow \frac{R}{100}=\frac{1}{10}\\ & \Rightarrow R=\frac{1}{10}\times 100\\ & =10\%\end{array}$$