Question

Pinky 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 were deducted for each wrong answer, then pinky again would have scored 40 marks. How many questions were there in the test?

Answer 1

Let the number of  right answers be x
And number of Wrong answers be y.

Total number of questions in the test= x+y

CONDITION 1.
Marks awarded for x right answers= 3x
Marks lost for y wrong answers = y×1= y
3x - y = 40………….(1)

CONDITION 2
Marks awarded for x right answers= 4x
Marks lost for y wrong answers = y×2= 2y
4x - 2y = 40…………(2)

Multiply equation 1 by 2 and subtract equation 2

6x - 2y = 80
4x - 2y = 40        [By elimination method]
(-)  (+)   (-)
-----------------
2x = 40
x = 40 /2
x = 20

On putting the value of x in equation 1.
3x -y = 40
3(20) - y = 40
60 - y = 40
-y  = 40 - 60
-y = -20
y = 20
Total number of questions in the test= x+y = 20 + 20= 40.

Hence, there were total 40 questions in the test

HOPE THIS WILL HELP YOU..

Answer 2

Let correct question = x

And incorrect question  = y
pinky scored 40 marks in a test, getting 3marks for each right answer and losing1 mark for each wrong answer.

3x -  y = 40

Subtract 3x both sides we get

-Y = 40 – 3x        

Change the sign we get

Y = 3x – 40 …(1)

Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then pinky would have scored 50 marks

We get

4x – 2y = 50

Plug the value of y we get

4x – 2(3x - 40) =50

4x – 6x + 80 = 50

-2x = - 30

X = 15

Plug this value back in equation first we get

Y = 3x – 40

Y = 3* 15- 40

Y = 45 – 40

Y = 5

So total question are x + y =  15 + 5 = 20