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?
(iii) Rakesh scores $18$ marks by attempting $16$ questions. How many questions has he attempted correctly and how many has he attempted incorrectly?

Answer 1

Marks obtained for $1$ right answer $=+3$

Marks obtained for $1$ wrong answer $=-2$

(i) Marks scored by Radhika $=20$

Marks obtained for $12$ correct answers $=12\times 3=36$

Marks obtained for incorrect answers $=$Total score $-$ Marks obtained for $12$ correct answers

$=20-36=-16$

Marks obtained for $1$ wrong answer $=-2$

Thus, number of incorrect answers $=(-16)÷(-2)=8$

Therefore, she attempted $8$ questions wrongly.

(ii) Marks scored by Mohini $=-5$

Marks obtained for $7$ correct answers $=7\times 3=21$

Marks obtained for incorrect answers = Total score − Marks obtained for $7$ correct answers

$=-5-21=-26$

Marks obtained for $1$ wrong answer $=-2$

Thus, number of incorrect answers $=(-26)÷(-2)=13$

Therefore, she attempted $13$ questions wrongly.

(iii) Total marks scored by Rakesh $=18$

Number of questions attempted $=16$

(Number of correct answers)$\left(3\right)+$(Number of incorrect answers)$(-2)=18$

⇒(Number of correct answers)$\left(3\right)+$($16-$ Number of correct answers)$(-2)=18$

⇒(Number of correct answers)$\left(3\right)+-32+2$(Number of correct answers)$=18$

⇒(Number of correct answers)$\left(5\right)+-32=18$

⇒(Number of correct answers)$\left(5\right)=18+32=50$

⇒ Number of correct answers $=10$

∴Number of incorrect answers $=16-10=6$

∴Total number of correct and incorrect answers scored by Rakesh is $10$ and $6$ respectively.