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 (Correct answer)
C. 84
D. 79
Correct Answer
Option B — 81
Detailed Solution & Explanation
The correct answer is Option B (81).
Key Points
Let C = correct, W = wrong. Then 5C − 2W = 69 and 4C − W = 84.
From the second, W = 4C − 84; substitute: 5C − 2(4C − 84) = 69 ⇒ −3C + 168 = 69 ⇒ C = 33, so W = 48.
Total questions = C + W = 33 + 48 = 81.
Additional Information
The student attempted all questions, so C + W equals the paper's size → Option B.