The simple interest on a certain sum of money at 5% per annum for 4 years and 3 years differs by Rs. 42. What is the sum?

Rs. 840

The correct answer is Option (1) → Rs. 840

To find the sum of money (Principal), we can use the formula for Simple Interest:

$SI = \frac{P \times R \times T}{100}$

1. Identify the given information:

• Rate ($R$): $5\%$ per annum
• Time 1 ($T_1$): $4$ years
• Time 2 ($T_2$): $3$ years
• Difference in Interest: $Rs.\ 42$

2. Set up the equation:

Let the sum of money be $P$. According to the problem:

$\text{Interest for 4 years} - \text{Interest for 3 years} = 42$

$\left( \frac{P \times 5 \times 4}{100} \right) - \left( \frac{P \times 5 \times 3}{100} \right) = 42$

3. Solve for $P$:

Simplify the terms:

$\frac{20P}{100} - \frac{15P}{100} = 42$

$\frac{5P}{100} = 42$

$\frac{P}{20} = 42$

$P = 42 \times 20$

$P = 840$