UPSC Prelims 2010 Q116: Science & Technology – Quantitative Aptitude
A candidate attempted 12 questions and secured full marks in all of them. If he obtained
60% marks in the test and all questions carried equal marks, then what is the total number of
questions in the test?
- (a) 36
- (b) 30
- (c) 25
- (d) 20
Answer: (d) 20
Explanation
Finding total questions from a percentage and a raw score
A candidate got full marks on 12 questions, which together equal 60% of the total marks.
| Step | Calculation |
|---|---|
| Let total questions = N | Each question has equal marks |
| Marks from 12 questions | Represents 60% of total marks |
| Equation | 12/N = 60/100 |
| Solve | N = 12 × 100/60 = 20 |
Why this works:
| Point | Detail |
|---|---|
| Equal marks per question | Lets us treat question count proportionally to marks |
| 12 questions = 60% of total | Directly gives N = 20 |
Answer: (d) 20.
Why each option is right or wrong
- (a) Incorrect. 36 would make 12 questions a much smaller percentage than 60%.
- (b) Incorrect. 30 would make 12 questions represent 40%, not 60%, of the total.
- (c) Incorrect. 25 would make 12 questions represent 48%, not 60%, of the total.
- (d) CORRECT. Solving 12/N = 60/100 gives N = 20, matching the given percentage exactly.
Key point
Since 12 fully-correct questions equal 60% of total marks (with equal marks per question), the total number of questions N satisfies 12/N = 60/100, giving N = 20.
Remember
12 fully-correct questions = 60% of total marks → total questions = 20.
Common mistakes
- Setting up the proportion equation incorrectly, inverting the percentage relationship.
- Forgetting that equal marks per question lets question count stand in directly for marks proportionally.
- Making a simple arithmetic error while solving for N.
Exam tip
'X questions = Y% of total, equal marks each' → total = X × 100/Y. A simple, frequently tested proportion setup.
Sources
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Percentage)
- NCERT Class VIII Mathematics — Comparing Quantities