If the difference between S.I. and C.I. for 2 years on a sum of money lent at 5% per annum is Rs. 6, then the sum is

Answer

To solve the problem, we need to find the principal amount (sum of money) based on the information given about the difference between Simple Interest (SI) and Compound Interest (CI) over 2 years at a rate of 5% per annum.

### Step-by-Step Solution:

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

2. **Given values**:
- The rate of interest \( r = 5\% \)
- The difference between CI and SI for 2 years is Rs. 6.

3. **Substituting the values into the formula**:
We substitute \( r = 5 \) into the difference formula:
\[ 6 = \frac{P \times 5^2}{100^2} \]

4. **Calculating \( 5^2 \) and \( 100^2 \)**:
\[ 5^2 = 25 \quad \text{and} \quad 100^2 = 10000 \]
Therefore, the equation becomes:
\[ 6 = \frac{P \times 25}{10000} \]

5. **Rearranging the equation to solve for \( P \)**:
Multiply both sides by 10000 to eliminate the fraction:
\[ 6 \times 10000 = P \times 25 \]
\[ 60000 = P \times 25 \]

6. **Dividing both sides by 25**:
\[ P = \frac{60000}{25} \]
\[ P = 2400 \]

### Conclusion:
The sum of money (principal amount) is Rs. 2400.