A student must score at least 50% to pass. He scored 50 marks, which is short of the passing marks by 50. What are the maximum marks of the paper?

Introduction / Context:
Translating passing criteria into an equation with maximum marks allows solving for the total marks. The statement indicates the student’s actual score is 50 below the passing threshold, which itself is 50% of the maximum marks.

Given Data / Assumptions:

• Pass percentage = 50%.
• Actual score = 50 marks.
• Short by 50 marks → Passing marks = 50 + 50 = 100.

Concept / Approach:
If passing marks are 50% of the maximum, then 0.50 * Max = 100. Solve for Max. This directly yields the total marks of the paper.

Step-by-Step Solution:

Verification / Alternative check:
With maximum 200, passing marks are 100. The student scored 50, which is indeed 50 below passing, matching the prompt.

Why Other Options Are Wrong:

• 250, 275, 300: At 50% pass, these would imply passing marks of 125, 137.5, or 150, contradicting the stated shortfall.

Common Pitfalls:
Misreading “short by 50” as “scored 50%,” or incorrectly combining the data. The phrasing means the pass mark is exactly 100.

Final Answer: