Let’s assume that the total number of correct answers be x and the total number of incorrect answers be y.
Hence, their sum will give the total number of questions in the test i.e. x + y
Further from the question, we have two type of marking scheme:
1) When 3 marks is awarded for every right answer and 1 mark deducted for every wrong answer.
According to this type, the total marks scored by Yash is 40. (Given)
So, the equation formed will be
3x – 1y = 40 ….. (i)
Next,
2) When 4 marks is awarded for every right answer and 2 marks deducted for every wrong answer.
According to this type, the total marks scored by Yash is 50. (Given)
So, the equation formed will be
4x – 2y = 50 …… (ii)
Thus, by solving (i) and (ii) we obtained the values of x and y.
From (i), we get
y = 3x – 40 …….. (iii)
Using (iii) in (ii) we get,
4x – 2(3x – 40) = 50
4x – 6x + 80 = 50
2x = 30
x = 15
Putting x = 14 in (iii) we get,
y = 3(15) – 40
y = 5
So, x + y
= 15 + 5
= 20
Therefore, the number of questions in the test were 20.