The difference of C.I and S.I on a sum at 5% per annum for 3 years is Rs. 1525. Find the sum.

Answer

To solve the problem of finding the sum where the difference between Compound Interest (C.I) and Simple Interest (S.I) at 5% per annum for 3 years is Rs. 1525, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Formula**:
The difference between Compound Interest and Simple Interest for 3 years can be calculated using the formula:
\[ \text{Difference} = \text{C.I} - \text{S.I} = \frac{P \times r^2}{100^2} \]
where \( P \) is the principal amount (the sum we need to find), and \( r \) is the rate of interest.

2. **Substituting the Known Values**:
Here, the rate \( r = 5\% \) and the difference is given as Rs. 1525. Therefore, we can substitute these values into the formula:
\[ 1525 = \frac{P \times (5)^2}{100^2} \]

3. **Calculating the Square of the Rate**:
Calculate \( (5)^2 = 25 \) and \( (100)^2 = 10000 \):
\[ 1525 = \frac{P \times 25}{10000} \]

4. **Rearranging the Equation**:
To isolate \( P \), multiply both sides by 10000:
\[ 1525 \times 10000 = P \times 25 \]
\[ 15250000 = P \times 25 \]

5. **Solving for \( P \)**:
Now, divide both sides by 25 to find \( P \):
\[ P = \frac{15250000}{25} \]
\[ P = 610000 \]

6. **Final Answer**:
Therefore, the sum (principal amount) is Rs. 610000.