A and B score 52\% and 67\% less than the maximum marks in an exam respectively. A's marks exceed the passing marks by 120, while B's marks fall short of the passing marks by 30. If C scores 54\% of the maximum marks, how many marks does C score more than the passing marks?

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**Solution:**

1. Let the maximum marks be denoted by $M$.

2. A gets 52\% less than maximum marks, so A's marks = $M - 0.52M = 0.48M$.

3. B gets 67\% less than maximum marks, so B's marks = $M - 0.67M = 0.33M$.

4. Let the passing marks be $P$.

5. Given A's marks are 120 more than passing marks:
   $$0.48M = P + 120$$

6. Given B's marks are 30 less than passing marks:
   $$0.33M = P - 30$$

7. Subtract the second equation from the first:
   $$0.48M - 0.33M = (P + 120) - (P - 30)$$
   $$0.15M = 150$$

8. Solve for $M$:
   $$M = \frac{150}{0.15} = 1000$$

9. Substitute $M = 1000$ into equation (5) to find $P$:
   $$0.48 	imes 1000 = P + 120$$
   $$480 = P + 120$$
   $$P = 360$$

10. C got 54\% of maximum marks:
    $$	ext{C's marks} = 0.54 	imes 1000 = 540$$

11. Marks C got more than passing marks:
    $$540 - 360 = 180$$

**Answer:** $180$

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