Question

Tara 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 wrong answer, then Tara would have scored 50 marks. Assuming that Tara attempted all question, find the total number of questions in the test. 

Answer 1

Let x be the number of Right Answer

y be the number of wrong Answer

∴ According to the question,

3x − y = 40         ...(i)

4x − 2y = 50       ...(ii)

Multiply with 2 in eq. (i)

6x − 2y = 80           ...(i)
4x − 2y = 50           ...(ii)
−   +     −       
          2x = 30    

x = 15

Putting the value of x in eqn. (i)

3 × 15 − y = 40
− y = 40 − 45
 y = 5

Total no. of question 

= 15 + 5

= 20