Explanation:

- 85% of the students passed the examination. This implies that 15% of the students failed.

- If 75 students failed, we use the relationship that 15% of the total students equals 75.

- To find the total number of students, calculate it as follows:

$$

\text{Total students} = \frac{75}{0.15} = 500

$$

- Correct Answer: Option 3 - 500

- Option 1 (480): If 480 students appeared, 15% would be 72, not 75.

- Option 2 (540): If 540 students appeared, 15% would be 81, more than 75.

- Option 4 (520): If 520 students appeared, 15% would be 78, more than 75.