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?
- (a) 99
- (b) 81 ✓ UPSC's answer
- (c) 84
- (d) 79
Why the answer is (b)
• Let c be correct and w wrong answers (all questions attempted).
• 5c − 2w = 69 and 4c − w = 84, so w = 4c − 84.
• Substituting: 5c − 8c + 168 = 69, so 3c = 99, c = 33 and w = 48.
• Total questions = 33 + 48 = 81: (b).
Why the other options are wrong
- (a) 99
- 99 does not satisfy both scoring equations.
- (c) 84
- 84 is the second score, not the number of questions.
- (d) 79
- 79 does not satisfy both scoring equations.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.