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
$\Rightarrow 3x - y = 40$
$3x - y - 40 ....(ii)$
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
$3 \times 15 - y - 40 = 0$
$45 - y - 40 = 0$
$-y + 5 = 0$
$y = 5$
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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