In a test, +3 marks are given for every correct answer and -1 mar…

Question

In a test, $+3$ marks are given for every correct answer and $-1$ mark are given for every incorrect answer. Sona attempted all the questions and scored $+20$ marks though she got $10$ correct answers. How many incorrect answers has she attempted$?$

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Answer

Let $x$ be the correct answers and $y$ be the incorrect answers, given by Sona.
It is given that, if she gives $10$ correct answers and her score is $20.$
Since, for every correct answer, $+3$ is given and for every incorrect answer, $-1.$ is given.
Hence, $3 \times ($Correct answer$) + (-1) \times ($Incorrect anwser$) =$ Total score
$\Rightarrow 3 \times 10 + (-1) \times y = 20$
$\Rightarrow 30 - y = 20$
$\Rightarrow 30 - 20 = y$
$\Rightarrow y = 10.$