Explanation:

To find the principal amount (P) needed to earn a simple interest of Rs5,040 over 3 years and 6 months at a rate of 12% per annum, follow these calculations:

- Formula: Simple Interest (SI) = P * R * T / 100

- Given: SI = Rs5,040, R = 12%, T = 3.5 years (3 years and 6 months)

- Rearrange the formula to find P: P = SI * 100 / (R * T)

- Substitute the values: P = 5,040 * 100 / (12 * 3.5)

Calculate:

- P = 5,040 * 100 / 42

- P = 12,000

Let's evaluate the options:

- Option 1: Rs9,000

- Option 2: Rs11,000

- Option 3: Rs15,000

- Option 4: Rs12,000 is correct as calculated.