The difference between CI and SI on a sum of money lent for 2 years at `10%` is ₹ 40. The sum is :

Options

A. 1600
B. 3000
C. 4000
D. none of these

Answer

To find the sum of money (the principal) based on the difference between compound interest (CI) and simple interest (SI) over 2 years at a rate of 10%, we can use the following steps:

### Step-by-Step Solution:

1. **Understanding the Formula**:
The difference between CI and 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. **Identifying the Given Values**:
From the problem, we know:
- The difference between CI and SI is ₹40.
- The rate of interest \( R = 10\% \).
- The time period is 2 years.

3. **Substituting the Values into the Formula**:
We can substitute the known values into the formula:
\[ 40 = \frac{P \times (10)^2}{(100)^2} \]

4. **Simplifying the Equation**:
This simplifies to:
\[ 40 = \frac{P \times 100}{10000} \]
\[ 40 = \frac{P}{100} \]

5. **Solving for Principal (P)**:
To find \( P \), we can multiply both sides of the equation by 100:
\[ P = 40 \times 100 \]
\[ P = 4000 \]

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

### Final Answer:
The sum is ₹4000.

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