Two candidates around the pass mark: One candidate scores 20% and fails by 50 marks. Another scores 40% and gets 30 marks more than the minimum required. Find the maximum marks of the exam.

Introduction / Context:
This problem frames two conditions around the pass mark. We express both in terms of the unknown maximum marks and solve simultaneously.

Given Data / Assumptions:

• Maximum marks = M; Pass mark = P.
• Candidate A: 20% of M is 50 below P ⇒ 0.2M + 50 = P.
• Candidate B: 40% of M is 30 above P ⇒ 0.4M = P + 30.

Concept / Approach:
Equate the two expressions for P from each condition to eliminate P and solve for M.

Step-by-Step Solution:

Verification / Alternative check:
Compute P from either equation: P = 0.2*400 + 50 = 80 + 50 = 130. Check B: 40% of 400 = 160, which is 30 more than 130 — consistent.

Why Other Options Are Wrong:

• 500, 450, 300, 350 do not satisfy both conditions simultaneously.

Common Pitfalls:
Misreading “fails by 50” and “gets 30 more than minimum” or mixing up which is percent of what.

Final Answer:
400