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?
Detailed Explanation:
Let correct answers = x, wrong answers = y. First condition: 5x - 2y = 69. Second condition: 4x - y = 84.
From second equation, y = 4x - 84. Substituting into first: 5x - 2(4x - 84) = 69 → 5x - 8x + 168 = 69 → -3x = -99 → x = 33. Thus y = 132 - 84 = 48.
Total questions = 33 + 48 = 81, making Option 2 the correct answer.
Question 2 of 4 Factors & Multiples
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