In an objective type question paper, 5 marks are awarded for a correct answer and 2 marks are deducted for a wrong answer. A student attempted all the questions and got a score of 69. Had he been awarded 4 marks for a correct answer and 1 mark deducted for a wrong answer, he would have scored 84. How many questions were there in the question paper?
Answer & explanation
Answer: (b) 81
With c correct and w wrong, 5c − 2w = 69 and 4c − w = 84. Solving gives c = 33 and w = 48, so the paper had 81 questions.
- 5c − 2w = 69 and 4c − w = 84.
- From the second: w = 4c − 84.
- Substitute: 5c − 8c + 168 = 69, so 3c = 99 and c = 33.
- w = 132 − 84 = 48.
- Total = 33 + 48 = 81.
- Check: 5 × 33 − 2 × 48 = 165 − 96 = 69.
Remember · Two scoring schemes for the same answers give two equations; solve for right and wrong counts, then add.
Question and answer: UPSC's provisional GS Paper II (2026, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·