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 ?
- (a) 9 ✓ UPSC's answer
- (b) 13
- (c) 27
- (d) 43
Why the answer is (a)
• Let the number of correct answers be C and the number of incorrect answers be I.
• Since all 90 questions were attempted, C + I = 90.
• The total score is calculated as 5C - 2I = 387.
• Substituting C = 90 - I into the score equation gives 5(90 - I) - 2I = 387.
• Simplifying yields 450 - 5I - 2I = 387, which leads to 7I = 63.
• Solving for I gives 9, which matches option (a).
Why the other options are wrong
- (b) 13
- 13 incorrect answers would result in a total score of 354, not 387.
- (c) 27
- 27 incorrect answers would result in a total score of 261, not 387.
- (d) 43
- 43 incorrect answers would result in a total score of 159, not 387.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2021, held on 10 October 2021. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.