(Q14).In a competitive exam, 3 marks are awarded for every correct answer and for every wrong answer, 1 mark will be deducted. Madhu scored 40 marks in this exam. Had 4 marks been awarded for each correct answer and 2 marks deducted for each incorrect answer, Madhu would have scored 50 marks. If Madhu has attempted all questions, how many questions were there in the test?

Let the number of correct answers be x

and the number of wrong answers be y.

When 3 marks are given for each correct answer and 1 mark deducted for each wrong answer, his score is 40 marks

So x - y = ...............(1)

His score would have been 50 marks if 4 marks were given for each correct answer and 2 marks deducted for each wrong answer

Thus, x - y = .................(2)

Substitution method

From equation (1), y = x -
Substituting in equation (2) 4x - 2 ( x - ) = 50

4x - x + = 50

- x = 50 - = -

x =
-
-2
 =

Substitute the value of x in equation (1)

3( ) - y = 40

- y = 40

y = - 40 =

∴ Total number of questions = + =