4. Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
(iii) 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?
Let the number of right answers and wrong answers be x and y respectively.
According to the question,
3x - y = 40 ... (i)
4x - 2y = 50
⇒ 2x - y = 25 ... (ii)
Subtracting equation (ii) from equation (i), we get
x = 15 ... (iii)
Putting this value in equation (ii), we get
30 - y = 25
y = 5
Therefore, number of right answers = 15
And number of wrong answers = 5
Total number of questions = 20
