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in Linear Equations by (56.3k points)

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?

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Let’s assume that the total number of correct answers be x and the total number of incorrect answers be y. 

Hence, their sum will give the total number of questions in the test i.e. x + y 

Further from the question, we have two type of marking scheme: 

1) When 3 marks is awarded for every right answer and 1 mark deducted for every wrong answer. 

According to this type, the total marks scored by Yash is 40. (Given) 

So, the equation formed will be 

3x – 1y = 40 ….. (i) 

Next, 

2) When 4 marks is awarded for every right answer and 2 marks deducted for every wrong answer. 

According to this type, the total marks scored by Yash is 50. (Given) 

So, the equation formed will be 

4x – 2y = 50 …… (ii) 

Thus, by solving (i) and (ii) we obtained the values of x and y. 

From (i), we get 

y = 3x – 40 …….. (iii) 

Using (iii) in (ii) we get, 

4x – 2(3x – 40) = 50 

4x – 6x + 80 = 50 

2x = 30 

x = 15 

Putting x = 14 in (iii) we get, 

y = 3(15) – 40 

y = 5 

So, x + y 

= 15 + 5 

= 20 

Therefore, the number of questions in the test were 20.

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