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  4. In a test of 50 questions, each correct answer fetches two marks and each wrong answer fetches -(1/2) marks. A candidate attempted all the questions and scored 40 mark. How many questions did he attempt correctly?

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Q. In a test of 50 questions, each correct answer fetches two marks and each wrong answer fetches $-\frac{1}{2}$ marks. A candidate attempted all the questions and scored 40 mark. How many questions did he attempt correctly?

Pair of Linear Equations in Two Variables

Solution:

Let the number of questions which are correct be $c$ and the questions which are wrong be $w$.
$c+w=50 $ (1)
$2 c-\frac{w}{2}=40$
$4 c-w=80$ (2)
From Eqs. (1) and (2), we have $\Rightarrow 5 c=130 \Rightarrow c=26$