In an objective type test of 90 questions, 5 marks are allotted for every correct answer and 2 marks are deducted for every wrong answer. After attempting all the 90 questions, a student got a total of 387 marks. What is the number of incorrect responses?
Answer & explanation
Answer: (a) 9
Full marks would be 90 × 5 = 450, and each wrong answer costs 5 + 2 = 7 marks compared with a right one. The shortfall of 63 marks means 9 wrong answers.
- If all 90 were correct: 90 × 5 = 450 marks.
- Each wrong answer loses 5 + 2 = 7 marks compared with a correct one.
- Shortfall = 450 − 387 = 63, so wrong answers = 63 ÷ 7 = 9.
- Check: 81 × 5 − 9 × 2 = 405 − 18 = 387.
Remember · Start from full marks and divide the shortfall by (marks for a correct answer + penalty for a wrong one).
Question and answer: UPSC's official GS Paper II (2021, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·