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 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?

Answer 1

Let number of correct answers be 'x' and number of incorrect answers be 'y'

As per given condition

$3x-y=\mathrm{40.....}\left(1\right)$

$4x-2y=\mathrm{50....}\left(2\right)$

Multiplying (1) by 2, we get

$6x-2y=\mathrm{80.....}\left(3\right)$

Now subtracting (2) from (3), we get

$6x-2y-4x+2y=80-50$

$2x=30$

$x=15$

putting the value of x in (1)

$y=3x-40$

$y=3\times 15-40$

$y=45-40$

$y=5$

Therefore total number of questions in the test $=15+5=20$