Yash scored 40 marks in a test, getting 3 marks for each right an… - Vidyadip

Question

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 awanded for each correct answer and 2 marks been deducted for each incorrect answer, the Yash would have scored 50 marks. How many question were there in the test?

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Answer

Let we taxe right answer be x then wrong answer will be y.
Therefore the total no. question = x + y ....(i)
It is given that if yash secord 40 marks in a test getting 3 marks for each right answer and losing 1 maks for each wrong answer then
⇒ 3x - y = 40
3x - y - 40 ....(ii)
It is also given that if 4 maks awarded for each right answer and 2 maks deducted for each wrong answer then he scored 50 marks.
4x - 2y = 50
4x - 2y - 50 ....(iii)
By multiplying eq. (ii) by 2 and we get
2(3x - y - 40)
= 6x - 2y - 80 = 0 .....(iv)
Now, subtracting eq. (iii) from eq. (iv)
6x - 2y - 80 - (4x - 2y - 50) = 0
6x - 2y - 80 - 4x + 2y + 50 = 0
2x - 30 = 0
2x = 30
x = 15
Now, Putting the value of x in eq. (ii) and we get
3 × 15 - y - 40 = 0
45 - y - 40 = 0
-y + 5 = 0
y = 5
Putting the value of x and y in eq. (i) and we get
x + y = 15 + 5 = 20
Hence, the total number of question is 20.

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