The simple interset on a certain sum at 5% per annum for 3 years and 4 years differ by Rs 42. The sum is :

Options

A. Rs 210
B. Rs 280
C. Rs 750
D. Rs 840

Answer

To solve the problem, we need to find the principal amount (sum) based on the information given about the simple interest for two different time periods.

### Step-by-Step Solution:

1. **Understand the Formula for Simple Interest (SI)**:
The formula for calculating simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
where \( P \) is the principal amount, \( R \) is the rate of interest per annum, and \( T \) is the time in years.

2. **Set Up the Equation for the Given Time Periods**:
Let the principal amount be \( P \).
- For 3 years, the simple interest will be:
\[ SI_3 = \frac{P \times 5 \times 3}{100} = \frac{15P}{100} = 0.15P \]
- For 4 years, the simple interest will be:
\[ SI_4 = \frac{P \times 5 \times 4}{100} = \frac{20P}{100} = 0.20P \]

3. **Set Up the Equation Based on the Difference**:
According to the problem, the difference in simple interest for 4 years and 3 years is Rs 42:
\[ SI_4 - SI_3 = 42 \]
Substituting the expressions for \( SI_4 \) and \( SI_3 \):
\[ 0.20P - 0.15P = 42 \]

4. **Simplify the Equation**:
\[ 0.05P = 42 \]

5. **Solve for \( P \)**:
To find \( P \), divide both sides by 0.05:
\[ P = \frac{42}{0.05} = 840 \]

6. **Conclusion**:
The principal amount (sum) is Rs 840.

### Final Answer:
The sum is Rs 840.