Exam qualification threshold and maximum marks It is required to score at least 40% to qualify. A candidate scored 200 marks and failed by 8 marks. What were the maximum marks for the exam?

Introduction / Context:
This aptitude question tests percentage application in exams. The key idea is that the qualifying cutoff is a fixed percentage of the maximum marks. If a candidate falls short by a given amount, we can back-calculate the maximum possible marks of the test paper using simple algebra with percentages.

Given Data / Assumptions:

• You must score 40% of the maximum marks to qualify.
• The candidate scored 200 marks.
• The candidate failed by 8 marks (i.e., needed 8 more marks to just qualify).
• Let the maximum marks be M (a positive number).

Concept / Approach:
The qualifying cutoff = 40% of M = 0.40 * M. “Failed by 8 marks” means the candidate’s score is 8 less than the cutoff. So candidate score + 8 = cutoff. From that, solve for M directly.

Step-by-Step Solution:
Let M be the maximum marks.Cutoff to qualify = 40% of M = 0.40 * M.Given: 200 is 8 less than the cutoff ⇒ 200 + 8 = 0.40 * M.Compute: 208 = 0.40 * M.Therefore M = 208 / 0.40 = 520.

Verification / Alternative check:
40% of 520 is 0.40 * 520 = 208. The candidate has 200, which is exactly 8 less than 208 as stated. This confirms the calculation is consistent.

Why Other Options Are Wrong:
540: 40% is 216, not 208; the shortfall would be 16, not 8.502: 40% is 200.8; shortfall would be 0.8, not 8.Couldn’t be determined: Sufficient data exists to find M uniquely.

Common Pitfalls:
Confusing “failed by 8” as “scored 8” or using 60% instead of 40%. Another error is subtracting 8 from the cutoff incorrectly or using 8% instead of 8 marks. Keep units straight: marks vs percentages.

Final Answer:
520