The difference between the compound interest and simple interest on a certain sum at 5% for 2 years is Rs. 1.50 the sum is

Answer

To solve the problem, we need to find the principal amount (P) given that the difference between the compound interest (CI) and simple interest (SI) for 2 years at a rate of 5% is Rs. 1.50.

### Step-by-Step Solution:

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

2. **Setting Up the Equation**:
Given that the difference is Rs. 1.50, we can set up the equation:
\[ \frac{P \times (5)^2}{100^2} = 1.50 \]
Simplifying this gives:
\[ \frac{P \times 25}{10000} = 1.50 \]

3. **Cross-Multiplying to Solve for P**:
To eliminate the fraction, we can cross-multiply:
\[ P \times 25 = 1.50 \times 10000 \]
This simplifies to:
\[ 25P = 15000 \]

4. **Isolating P**:
Now, divide both sides by 25 to solve for \( P \):
\[ P = \frac{15000}{25} \]
Calculating this gives:
\[ P = 600 \]

5. **Conclusion**:
The principal amount \( P \) is Rs. 600.

### Final Answer:
The sum is Rs. 600.

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