Question

Form the pair of linear equations & find their solutions by elimination 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?

[Class 10 NCERT Ch:3]

Answer 1

Hi govind,
here is the required answer:-

Let the number of correct answers be 'x'
Then the number of incorrect answers be 'y'

According to the question,
3 marks for each right answer and losing 1 mark for each wrong answer.

Then the equation would be
3x - y = 40 -----------(1)

Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer,

For this the equation would be
4x-2y=50
2(2x-y)=2(25)
2x-y=25 ----------------(2)

Solving by elimination method,
(2)-(1)

2x-y = 25
3x-y= 40
_______
-x=-15
x=15

Substitute x value in (2),we get

2(15)-y=25
y=30-25
y=5

Therefore,the number of correct answers=15
Number of incorrect answers=5

Total no,of questions=15+5=20

★Hope it helps★

Answer 2

♠Answer♠

That's a simple one .

Let 'x' Be the Correct Answers & 'y' be The Wrong Ones .

Than , By The First Statement ,

3x - y = 40

And , By Second Statement ,

4x - 2y = 50

So , Multiplying the First Statement by 2 ,

6x - 2y = 80

subtracting the second Equation from It ,

2x = 30

x = 15

& y = 5

Hence , Total Questions ,

x + y = 20 .

#SupermanINFINITY