Explanation:

- The student failed by 24 marks, meaning they needed 224 marks to pass.

- That 224 marks is 35% of the total maximum marks.

- To find the maximum marks, set up the equation: 35% of X = 224.

- Solve for X: X = 224 / 0.35 = 640.

- Option 1: 820 - Too high, not right.

- Option 2: 600 - Too low, doesn't match the requirement.

- Option 3: 610 - Still too low.

- Option 4: 640 - Matches our calculation and fulfills the problem requirement.