Question

Question 4 (iii)
Form the pair of linear equations for the following problem and find their solution (if they exist) by any algebraic method:
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?
Assume Yash answered all the questions.

Answer 1

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
$\Rightarrow$ 2x - y = 25 ... (ii)
Subtracting equation (ii) from equation (i), we get
3x - y -(2x - y) = 40 -25
$\Rightarrow$ 3x - y -2x + y = 15
$\Rightarrow$ x = 15 ... (iii)
Putting this value in equation (ii), we get
2(15) - y = 25
$\Rightarrow$ 30 - y = 25
$\Rightarrow$ y = 5
Therefore, number of right answers is x = 15 and number of wrong answers is y = 5
Total number of questions is x + y = 15 + 5 = 20.