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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?

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Solution

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 =12×3=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 =7×3=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)(3)+(Number of incorrect answers)(−2)=18

⇒(Number of correct answers)(3)+(16− Number of correct answers)(−2)=18

⇒(Number of correct answers)(3)+−32+2(Number of correct answers)=18

⇒(Number of correct answers)(5)+−32=18

⇒(Number of correct answers)(5)=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.

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