Question

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

- 10
- 20
- 25
- 30

Hint:

### A mathematical definition of an equation is a claim that two expressions are equal and joined by the equals sign. We have to find the number of questions that were there in the test. Here we will create some equations and then find the values of the variables created.

## The correct answer is: 20

### Now here we have given In a competitive exam, 3 marks are to be awarded for every correct answer and for every wrong answer, 1 mark will be deducted Madhu scored 40 marks in the exam Had 4 marks been awarded for each correct answer and 2 marks deducted for each incorrect answer.

So let the number of correct answers be x and the number of wrong answers be y.

As per the condition, when 3 marks are given for each correct answer and 1 mark deducted, for each wrong answer , his score is 40 marks, so the equation becomes:

3x - y = 40 ................................ (a)

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

4x - 2y = 50 ................................ (b)

Let's use the substitution method :

Putting y = 3x - 40 in equation (b), we get:

4x - 2( 3x - 40 ) = 50

4x - 6x + 80 = 50

-2x = 50 - 80

-2x = -30

x = ( -30 )/( -2 )

x = 15

Now substituting the value of x in equation (a), we get:

3( 15 ) - y = 40

45 - y = 40

- y = 40 - 45

- y = -5

y = 5

Total number of questions = x + y

= 15 + 5

= 20

So here we used the substitution method to solve the question, apart from this method we can also use the elimination method to solve the problem as we have variables here. So there were 20 questions that were there in the test.

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