There are 40 questions in the test booklet of Maths olympiad. If stephen attempts all the questions and scores 80 marks when 5 marks are awarded for each correct answer and 3 marks is deducted for each incorrect answer then find the number of correct answer attempted by stephen
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Answer:
Let us assume the correct answers as "x" and wrong answers as "y".
According to question,
(i) Total number of questions in the test:
⇒ x + y = 40 .
(ii) 5 marks are awarded for correct answer and 3 marks for wrong answer. He scores 80 marks.
⇒ 5x - 3y = 80
On solving (i) * 5 & (ii), we get
⇒ 5x + 5y = 200
⇒ 5x - 3y = 80
-------------------
8y = 120
y = 15.
Substitute y = 15 in (ii), we get
⇒ 5x - 3y = 80
⇒ 5x - 45 = 80
⇒ 5x = 125
⇒ x = 25.
Therefore:
⇒ Number of correct answers = 25
⇒ Number of incorrect answers = 15.
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