The simple interest on a sum of money for 2 years at a certain rate of interest is ₹320. The compound interest, compounded annually on the same sum for the same duration and at the same rate of interest is ₹384. The sum (in ₹) is:

P = principal amount

R = rate of interest

T = time

The simple interest on a sum of money for 2 years at a certain rate of interest is ₹320.

$$interest\ =\ \frac{\left(P\times\ R\times\ T\right)}{100}$$

$$320\ =\ \frac{\left(P\times\ R\times\ 2\right)}{100}$$

$$160\ =\ \frac{PR}{100}$$

PR = 16000

$$R=\frac{16000}{P}$$    Eq.(i)

The compound interest, compounded annually on the same sum for the same duration and at the same rate of interest is ₹384.

$$interest+P\ =\ P\left(1+\frac{R}{100}\right)^T$$

$$384+P\ =\ P\left(1+\frac{R}{100}\right)^2$$

Put Eq.(i) in the above equation.

$$384+P\ =\ P\left(1+\frac{\frac{16000}{P}}{100}\right)^2$$

$$384+P\ =\ P\left(1+\frac{160}{P}\right)^2$$
$$P^2+384P=P^2+320P+25600$$

384P-320P = 25600

64P = 25600

P = ₹400