Yash scored 80 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awanded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 100 marks. How many questions were there in the test?

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Solution

Let x be the number of correct answers and y be the number of wrong answers.
As per the question,
3x - 1y = 80 ....(1)
4x - 2y = 100 ....(2)

Multiplying equation (1) by 2,

6x - 2y = 160 ....(3)

Subtracting equation (2) from (3),

2x = 60

$\Rightarrow$ x = 30

$∴$ y = 3x - 80 = 10

So, total number of questions = 10+30 = 40

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