In a class test (+6) marks are given for every correct answer and… - Vidyadip

Question

In a class test (+6) marks are given for every correct answer and (-2) marks are given for every incorrect answer and no marks for not attempting any question.
(i) Shreya scored 40 marks. If she has got 10 correct answers, how many questions has she attempted incorrectly?
(ii) Shreya scored 24 marks by attempting 8 questions. How many questions has she attempted correctly and how many questions has she attempted incorrectly?

✓

Answer

(i) Marks for each correct answer $=+6$
Marks for each incorrect answer $=-2$
Shreya's marks for correct answer $=10 \times 6$ points
$=60$ points
Since, Shreya's scored $=40$ marks
$\therefore$ Shreya's marks for incorrect answer
$
=40-60=-20
$
$\therefore$ Incorrect answer attempted by Shreya $=\frac{-20}{-2}=10$
Thus, Shreya attempted 10 incorrect answers.
(ii) Let correct answers attempted by Shreya is $x$.
Then, Incorrect answers $=8-x$
Marks scored for correct answers $=6 \times x=6 x$
and marks scored for incorrect answers
$
=(-2) \times(8-x)=-16+2 x
$
Since, Shreya scored $=24$ marks
According to the question,
$6 x+2 x-16=24$
$\begin{array}{ll}\Rightarrow & 8 x=24+16 \\ \Rightarrow & 8 x=40 \Rightarrow x=5\end{array}$
$\therefore$ Shreya attempted 5 correct and 3 incorrect answers.

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