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Q.


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. What is the number of questions present in the test?

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a

15

b

10

c

20

d

25 

answer is C.

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Detailed Solution

Given that the Yash scored 40 marks on a test, and he gets 3 marks for each right answer and lost 1 mark for each wrong answer.
Let the number of correct answers is x and the number of incorrect answers is y.
Then, the total number of questions in the test = x + y.
As Yash scored 40 marks with given condition,
⇒3x−y=40            ----(i)
Now, when 4 marks had been given for each correct answer and 2 marks get deducted for each incorrect answer then the score of Yash will become 50 marks.
⇒4x−2y=50             ----(ii)
Let us use the substitution method to determine the value of x and y.
On subtracting (i) from (ii), we get
4x−2y=50 3x−y=40 ¯   x−y=10 ⇒x=10+y    -------(iii)              
On putting the value of x in equation (i) we get,
3 10+y −y=40 30+3y−y=40 2y=40−30  
y= 10 2 y=5  
To determine the value of x, we put the value of y in equation (iii).
x=10+y  
⇒x=10+5 ⇒x=15  
We know that the total number of questions in the test are x + y.
So, putting the values of x and y in the above equation,
⇒x+y=15+5 ⇒x+y=20  
Hence the total number of questions in the test is 20.
Therefore, the correct option is 3.
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