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Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

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Given:

Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks.

To find:

How many questions were there in the test?

Solution:

Let the number of right answers be ‘a’ and number of wrong answers be ‘b’

Given, Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Deducted marks are represented by "-" sign.

⇒ 3a – b = 40 ------ (1)

Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks

⇒ 4a – 2b = 50 ---- (2)

Multiplying eq1 by 2 and subtracting eq2 from it

⇒ 4a - 2b - 2(3a - b) = 50 - 2(40)

⇒ 4a - 2b - 6a +2b = 50 - 80

⇒ 4a - 6a = 50 - 80

⇒ 6a – 4a = 80 – 50

⇒ 2a = 30

⇒ a = 15

Put the value of a in eq. 1 to get,

3(15) - b = 40

⇒ 45 - b = 40

⇒ - b = 40 - 45

⇒ - b = - 5

⇒ b = 5

Total number of questions in the test = right answers + wrong answers = a + b = 15 + 5 = 20

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