If the difference between the compound and simple interests on a certain sum of money for 2 years at 20% per annum is ₹64, then the sum in ₹ will be:

1600

The correct answer is Option (4) → 1600

For 2 years, the difference between Compound Interest (CI) and Simple Interest (SI) is given by:

$\text{CI} - \text{SI} = P \left(\frac{r}{100}\right)^2$

Given:

• Rate $r = 20\%$
• Difference = ₹64

Step 1: Substitute values

$64 = P \left(\frac{20}{100}\right)^2$

$64 = P \times \left(\frac{1}{5}\right)^2$

$64 = P \times \frac{1}{25}$​

Step 2: Find P

$P = 64 \times 25 =1600​$