The difference between CI and S I for 2 years at 10% rate of interest is Rs. 4. Find the sum of money.

Options

A. Rs. 400
B. Rs. 200
C. Rs. 300
D. Rs. 800

Answer

To solve the problem, we need to find the sum of money (principal) given that the difference between Compound Interest (CI) and Simple Interest (SI) for 2 years at a rate of 10% is Rs. 4.

### Step-by-Step Solution:

1. **Understand the Formula for the Difference Between CI and SI**:
The difference between Compound Interest (CI) and Simple Interest (SI) for 2 years can be calculated using the formula:
\[ \text{Difference} = \frac{P \times R^2}{100^2} \]
where \( P \) is the principal amount, and \( R \) is the rate of interest.

2. **Substitute the Given Values**:
We know that the difference is Rs. 4, and the rate \( R \) is 10%. Therefore, we substitute these values into the formula:
\[ 4 = \frac{P \times 10^2}{100^2} \]

3. **Simplify the Equation**:
Calculate \( 10^2 \) and \( 100^2 \):
\[ 10^2 = 100 \quad \text{and} \quad 100^2 = 10000 \]
Substitute these values back into the equation:
\[ 4 = \frac{P \times 100}{10000} \]

4. **Further Simplification**:
Simplifying the right side:
\[ 4 = \frac{P}{100} \]

5. **Solve for \( P \)**:
To find \( P \), multiply both sides of the equation by 100:
\[ P = 4 \times 100 \]
\[ P = 400 \]

6. **Conclusion**:
The sum of money (principal) is Rs. 4000.

### Final Answer:
The sum of money is Rs. 4000.