Question

In a class test $(+3)$ 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) Radhika scored $20$ marks. If she has got $12$ correct answers, how many questions has she attempted incorrectly? (ii) Mohini scores $(-5)$ marks in this test, though she has got $7$ correct answers How many questions has she attempted incorrectly.

Answer 1

Given, In a class test, the marks allotted is $+3$ for each correct answer,
$-2$ for each incorrect answer and no marks for not attempting any question.
1) Since, Radhika final score $=20$ marks, in which number of correct answers are $=12$
So, the marks obtained for $12$ correct answers $=12\times 3$
$=36$ marks as $3$ marks for each correct answer.
Since, Negative marks $=$ marks for all correct answers $-$final score
Thus, negative marks $=36-20=16$

Therefore, she got $16$ marks negative.
Since, $-2$ marks for each incorrect answer.

Therefore, she made $\frac{16}{2}=8$ incorrect answers.

2) Given, Mohini final score $=-5$, in which number of correct answer are $7$.
Mohini score for all correct answers $=7\times 3=21$ marks, as $3$ marks for each correct answer.

Since, Negative marks$=$ marks for correct answers$-$final score
$=21-(-5)$
$=21+5$

$=26$ marks.

Thus, she got $26$ marks negative.
Since, $-2$ marks for each incorrect answer.

Therefore, she made $\frac{26}{2}=13$ incorrect answers.