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.
Aptitude
Percentage
Difficulty: Medium
Choose an option
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A500
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B450
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C300
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D400
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E350
Answer
Correct Answer: 400
Explanation
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:
From A: P = 0.2M + 50.From B: P = 0.4M − 30.Equate: 0.2M + 50 = 0.4M − 30 ⇒ 0.2M = 80 ⇒ M = 400.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