Explanation:

- Let's denote the number of students who passed as \(x\) and those who failed as \(150 - x\).

- The total marks for 150 students is 150 * 40 = 6000.

- Passed students have an average of 60 marks, so their total marks are \(60x\).

- Failed students have an average of 20 marks, so their total marks are \(20(150 - x)\).

- The equation is \(60x + 20(150 - x) = 6000\).

- Simplifying the equation: \(60x + 3000 - 20x = 6000\).

- Further simplification leads to \(40x = 3000\).

- Solving gives \(x = 75\).

- Option 3: 75 is the correct answer.