Form the pair of linear equations in the following problems and find their solutions (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?

#### Solution

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