In an examination, there were 75 questions. 3 marks were awarded for each correct answer, 1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question. Rayan scored a total of 97 marks in the examination. If the number of unattempted questions was higher than the number of attempted questions, then the maximum number of correct answers that Rayan could have given in the examination is:
Explanation:
Let the number of correct, wrong and un-attempted questions be c, w and u respectively. Since u > c + w ⇒ u > 75 - u ⇒ u > 37.5 ∴ Least possible value of u is 38
⇒ c + w + u = 75 …(1) ⇒ 3c – w + u = 97 …(2)
(2) + (1) ⇒ 4c + 2u = 172 ⇒ 2c + u = 86 ⇒ 2c = 86 - u
c will be greatest when u is least i.e., u = 38
⇒ 2c = 86 - 38 = 48 ⇒ c = 24
∴ Maximum value c can take is 24.
Hence, 24.
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