If the difference CI and SI on a certain sum of money for 3 years at 5% per annum is Rs. 122 find the sum.

Answer

To solve the problem of finding the principal amount based on the difference between Compound Interest (CI) and Simple Interest (SI) over 3 years at a rate of 5% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for the Difference Between CI and SI**:
The difference between Compound Interest and Simple Interest for 3 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. **Identify Given Values**:
From the problem, we have:
- Difference = Rs. 122
- Rate (R) = 5%
- Time (T) = 3 years

3. **Substitute the Values into the Formula**:
Plugging the known values into the formula:
\[ 122 = \frac{P \times 5^2}{100^2} \]

4. **Calculate \( R^2 \) and \( 100^2 \)**:
Calculate \( 5^2 \) and \( 100^2 \):
\[ 5^2 = 25 \quad \text{and} \quad 100^2 = 10000 \]
So the equation becomes:
\[ 122 = \frac{P \times 25}{10000} \]

5. **Rearranging the Equation**:
Rearranging the equation to solve for \( P \):
\[ P = \frac{122 \times 10000}{25} \]

6. **Calculate \( P \)**:
Now, perform the multiplication and division:
\[ P = \frac{1220000}{25} = 48800 \]

7. **Final Result**:
Therefore, the principal amount \( P \) is Rs. 48800.

### Summary of the Solution:
The sum of money (principal) is Rs. 48800.