Passing threshold from fail data: A student must score 40% to pass. He scores 40 marks and fails by 40 marks. What are the maximum marks of the exam?

Introduction / Context:
We will use the relationship between required pass percentage, maximum marks, and the student’s shortfall.

Given Data / Assumptions:

• Pass mark = 40% of maximum marks M.
• Student’s actual marks = 40.
• He fails by 40 marks ⇒ Pass mark = 40 + 40 = 80.

Concept / Approach:
Set 0.40 * M = 80 and solve for M.

Step-by-Step Solution:

Verification / Alternative check:
40% of 200 = 80. Candidate had 40, short by 40 — matches the statement.

Why Other Options Are Wrong:

• 250, 300, 150, 400 do not yield a pass mark of 80 at 40%.

Common Pitfalls:
Confusing “fails by 40” with “scored 40%” or misplacing what the 40 refers to.

Final Answer:
200