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

Options

A. Rs.2200
B. Rs.2400
C. Rs.2600
D. Rs.2000

Answer

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

### Step-by-Step Solution:

1. **Understanding the Formula for Difference between CI and SI**:
The difference between Compound Interest (CI) and Simple Interest (SI) for 2 years can be given by 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. **Substituting the Known Values**:
From the problem, we know:
- The difference is Rs. 6.
- The rate \( R \) is 5%.
Substituting these values into the formula:
\[ 6 = \frac{P \times 5^2}{100^2} \]

3. **Calculating \( 5^2 \) and \( 100^2 \)**:
Calculate \( 5^2 \) and \( 100^2 \):
\[ 5^2 = 25 \quad \text{and} \quad 100^2 = 10000 \]
So, we can rewrite the equation as:
\[ 6 = \frac{P \times 25}{10000} \]

4. **Rearranging the Equation**:
To isolate \( P \), we multiply both sides by 10000:
\[ 6 \times 10000 = P \times 25 \]
This simplifies to:
\[ 60000 = P \times 25 \]

5. **Solving for \( P \)**:
Now, divide both sides by 25 to find \( P \):
\[ P = \frac{60000}{25} \]
Performing the division:
\[ P = 2400 \]

### Final Answer:
The sum of money (the principal amount) is Rs. 2400.