Pass threshold shortfall: To pass, 36% of the maximum marks is required. A student scored 113 and fell short by 85 marks. What are the maximum marks?

Introduction / Context:
Here we relate a fixed passing percentage to a student’s mark and shortfall. The pass mark equals the student’s score plus the shortfall; compute the maximum from the pass percentage.

Given Data / Assumptions:

• Pass mark = 36% of maximum marks.
• Student’s score = 113.
• Shortfall to pass = 85 ⇒ pass mark = 113 + 85 = 198.

Concept / Approach:
Let maximum marks be M. Then 0.36M = 198. Solve for M by dividing both sides by 0.36. Ensure correct base (maximum marks) for the pass percentage.

Step-by-Step Solution:
0.36M = 198M = 198 / 0.36 = 550

Verification / Alternative check:
36% of 550 = 198. The student at 113 is short by 85, matching the given condition.

Why Other Options Are Wrong:
500, 640, 1008, 480 do not yield a pass mark of 198 at 36%.

Common Pitfalls:
Using 36% of the student’s marks or adding 36 to the score. Passing percentage always applies to the maximum possible marks.

Final Answer:
550