The simple interest on a certain sum for 2 years is Rs.400 and the compound interest is Rs.410. find the rate of interest per annum.

Correct option is B

​$$\text{Given:} \\\text{SI}_{2\text{ years}} = 400, \quad \text{CI}_{2\text{ years}} = 410 \\\text{Time} = 2 \text{ years} \\\text{Difference between CI and SI:} \\\text{CI} - \text{SI} = 410 - 400 = 10 \\\text{We know:} \\\text{Difference} = P \times \left(\frac{R}{100}\right)^2 \quad \text{(1)} \\\text{Also, Simple Interest formula:} \\\text{SI} = \frac{P \times R \times T}{100} \\\Rightarrow 400 = \frac{P \times R \times 2}{100} \quad \text{(2)} \\\text{From (2):} \\P \times R = 400 \times \frac{100}{2} = 20000 \\\Rightarrow P = \frac{20000}{R} \\\text{Substitute into (1):} \\\text{CI} - \text{SI} = \frac{20000}{R} \times \left(\frac{R}{100}\right)^2 = 10 \\\Rightarrow \frac{20000}{R} \times \frac{R^2}{10000} = 10 \\\Rightarrow \frac{20000 \times R}{10000} = 10 \\\Rightarrow 2R = 10 \\\Rightarrow R = 5$$​​