The difference between simple interest and compound interest of a certain sum of money at 20% per annum for 2 years is Rs. 48. Then the sum is

Options

A. `Rs. 1,000`
B. Rs. 1,200
C. Rs. 1,500
D. Rs. 2,000

Answer

To solve the problem, we need to find the principal sum of money (P) given that the difference between the simple interest (SI) and compound interest (CI) for 2 years at a rate of 20% per annum is Rs. 48.

### Step-by-Step Solution:

1. **Understand the Formula for Simple Interest and Compound Interest:**
- Simple Interest (SI) for 2 years is given by the formula:
\[ SI = \frac{P \times R \times T}{100} \]
where \( P \) is the principal, \( R \) is the rate of interest, and \( T \) is the time in years.
- For 2 years, the formula becomes:
\[ SI = \frac{P \times 20 \times 2}{100} = \frac{40P}{100} = \frac{2P}{5} \]

2. **Calculate Compound Interest for 2 Years:**
- The formula for Compound Interest (CI) for 2 years is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
- For 2 years at 20%:
\[ CI = P \left(1 + \frac{20}{100}\right)^2 - P = P \left(1.2\right)^2 - P = P(1.44) - P = 0.44P \]

3. **Find the Difference between CI and SI:**
- The difference between CI and SI is given as:
\[ CI - SI = 0.44P - \frac{2P}{5} \]
- To simplify \(\frac{2P}{5}\), convert it to a decimal:
\[ \frac{2P}{5} = 0.4P \]
- Therefore, the difference becomes:
\[ 0.44P - 0.4P = 0.04P \]

4. **Set the Difference Equal to Rs. 48:**
- According to the problem, this difference is Rs. 48:
\[ 0.04P = 48 \]

5. **Solve for P:**
- To find \( P \), divide both sides by 0.04:
\[ P = \frac{48}{0.04} = 1200 \]

### Conclusion:
The sum of money (P) is Rs. 1200.