Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer.

Question

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 ?

Answer 1

Let the number of right answers be ‘x’, and the number of wrong answers be y’. 

3x – y = 40 ……….. (i) 

4x – 2y = 50 ………. (ii) 

By Elimination method we can find our solution : 

3x – y = 40 ……… (i) 

2x – y = 25 ……….. (ii) 

Subtracting eqn. (ii) from eqn. (i),

Substituting the value of ‘x’ in eqn. (i), 

3x – y = 40 

3(15) – y = 40 

45 – y = 40 

-y = 40 – 45 

-y = -5 

∴ y = 5 

Questions of right answers, x = 15 

Questions of wrong answers, y = 5 

∴ Total number of questions = x + y = 15 + 5 = 20