Explanation:

- To find the amount, we start by calculating the difference in simple interest.

- The formula for simple interest is \( \text{SI} = \frac{P \times R \times T}{100} \).

- Let \( P \) be the principal amount.

- For 6 years, the interest: \( \text{SI}_1 = \frac{P \times 4 \times 6}{100} \).

- For 11 years, the interest: \( \text{SI}_2 = \frac{P \times 4 \times 11}{100} \).

- The difference: \( \text{SI}_2 - \text{SI}_1 = 7500 \).

- Set up the equation:

- \(\frac{P \times 4 \times 11}{100} - \frac{P \times 4 \times 6}{100} = 7500\).

- Solve for \( P \):

- Simplify: \(\frac{P \times 4 \times (11 - 6)}{100} = 7500\).

- \(\frac{P \times 20}{100} = 7500\).

- \(P = \frac{7500 \times 100}{20}\).

- \(P = 37,500\).

- Options Check:

- 1. Rs.38,000

- 2. Rs.37,500

- 3. Rs.37,000

- 4. Rs.38,500

- The correct amount is: Rs.37,500