A student scored 57 marks in a test, getting 4 marks for each right answer and losing 1 mark for each wrong answer. Had 3 marks been awarded for each correct answer and 1 marks been deducted for each incorrect answer, then she would have scored 40 marks. How many questions were there in the test?
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Let the no. of right answers be a and no. of wrong answers be b.
Therefore, the student would get 4a marks for all his right answer and b marks would be deducted for all his wrong answers.
So, 4a - b = 57 - ( i )
In the new system, the student would get 3a marks for all his right answers and b marks would be deducted for all his wrong answers.
So, 3a - b = 40 - ( ii )
From i and ii,
4a - b = 57
3a - b = 40
- + -
----------------
a = 17
4a - b = 57
b = 4×17 - 57
b = 68 - 57
b = 11
Therefore, there are a + b = 17 + 11 = 28 questions in the test.
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