Question

Yash scored $40$ marks in a test 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 deduced for each incorrect answer, then Yash would have scored $50$ marks. How many questions were there in the test?

• A. $30$
• B. $10$
• C. $20$
• D. $40$

Answer 1

The correct option is C $20$

Let $x$ be the number of questions of right answer and $y$ be the number of questions of wrong answer.
According to question,
$3x-y=40$ ...(i)
and $4x-2y=50$
or $2x-y=25$ ....(ii)
Subtracting (ii) from (i), we have
Putting the value of $x$ in equation (i), we have
$3\times 15-y=40\Rightarrow 45-y=40$
$\therefore y=45-40=5$
Hence, total number of questions is $x+y$ i.e., $5+15=20$