Simran has a certain sum deposited in a bank at `5%` per annum. Rajat also have the same sum deposited in the same bank at `9%` per annum. The difference between the annual interest received by both of them is Rs. 220. Find the sum.

Options

A. Rs. 4500
B. Rs. 5500
C. Rs. 6792
D. Rs. 10000

Answer

To solve the problem, let's denote the sum deposited by both Simran and Rajat as \( P \).

1. **Calculate the annual interest for Simran**:
Simran's interest at 5% per annum can be calculated using the formula:
\[ \text{Interest} = \frac{P \times \text{Rate} \times \text{Time}}{100} \]
For Simran:
\[ \text{Interest}_{\text{Simran}} = \frac{P \times 5 \times 1}{100} = \frac{5P}{100} = 0.05P \]

2. **Calculate the annual interest for Rajat**:
Rajat's interest at 9% per annum can be calculated similarly:
\[ \text{Interest}_{\text{Rajat}} = \frac{P \times 9 \times 1}{100} = \frac{9P}{100} = 0.09P \]

3. **Set up the equation for the difference in interest**:
According to the problem, the difference between the annual interest received by Rajat and Simran is Rs. 220. Therefore, we can set up the equation:
\[ \text{Interest}_{\text{Rajat}} - \text{Interest}_{\text{Simran}} = 220 \]
Substituting the values we calculated:
\[ 0.09P - 0.05P = 220 \]

4. **Simplify the equation**:
Simplifying the left side:
\[ 0.04P = 220 \]

5. **Solve for \( P \)**:
To find \( P \), divide both sides of the equation by 0.04:
\[ P = \frac{220}{0.04} \]
Calculating this gives:
\[ P = 5500 \]

So, the sum deposited by both Simran and Rajat is Rs. 5500.