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