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?

To find: Number of questions in a test.

Explanation:

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

= 15 + 5

= 20