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UPSC Prelims 2026 CSAT, question 38

Topic: Arithmetic

Q38

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?

  1. (a) 99
  2. (b) 81Correct answer
  3. (c) 84
  4. (d) 79

Solution.

Answer: (b) 81

  1. Let cc be the number of correct answers and ww be the number of wrong answers; then 5c−2w=695c - 2w = 69 and 4c−w=844c - w = 84.
  2. Substituting w=4c−84w = 4c - 84 into the first equation gives 5c−2(4c−84)=69⇒168−3c=69⇒3c=99⇒c=335c - 2(4c - 84) = 69 \Rightarrow 168 - 3c = 69 \Rightarrow 3c = 99 \Rightarrow c = 33.
  3. Then w=4(33)−84=48w = 4(33) - 84 = 48, so the total number of questions is c+w=33+48=81c + w = 33 + 48 = 81.