Question

In a test, $4$ marks are given for every correct answer and $-2$ marks, for every incorrect answer. Asha answered all the questions and scored $26$ marks though she got nine correct answers. Varun also answered all the questions and scored $2$ marks though he got five correct answers. How many questions did each answer incorrectly?

• A. $10,8$
• B. $9,18$
• C. $5,9$
• D. $4,10$

Answer 1

Answer: (C)

$5,9$

Case $1$: Asha scored $=26$ marks
Correct answer by Asha $=9$
Let incorrect answers by Asha be $x$
According to question, $9\left(4\right)+x(-2)=26$
$-2x=26-36$
$\Rightarrow x=5$.
Incorrect answers by Asha $=5$

Case $2$: Varun scored $=2$ marks
Correct answers by Varun $=5$
Let incorrect answers by Varun be $y$
According to question, we have
$5\left(4\right)+y(-2)=2\Rightarrow -2y=2-20\Rightarrow y=9$
Incorrect answers by Varun $=9$.