Question
In a competitive examination containing 100
questions, 1 mark is awarded for every correct answer and ½ mark gets deducted for every wrong answer. If a student attempted all questions and obtained 79 marks, how many wrong answers must he have given?Solution
Let number of questions with right answers = x ∴ No. of questions with wrong answers = 100 – x ∴ Marks obtained for right answers = x ∴ Marks deducted for wrong answers = (100 - x)/ 2 ∴ x - (100 - x) / 2 = 79 ⇒ 2x - 100 + x/ 2 = 79 ⇒ 3x - 100 = 158 ⇒ 3x = 258 ∴ x = 86 ∴ No. of questions with wrong answers (100 – 86) = 14
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