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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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(i) Let `x` is the number of questions that Radhika answered incorrectly.
Then,
`12(3) + (-2)x = 20`
`2x = 16=>x = 8`

(ii)Let `y` is the number of questions that Mohini answered incorrectly.
Then,
`7(3) + (-2)x = -5`
`2x = 26=>x = 13`

(iii)Let `a` is the number of questions that Rakesh answered correctly.
Then, `16-a` is the number that he attempted incorrectly.
Then,
`3a+(-2)(16-a) = 18`
`3a+2a-32 = 18=> 5a = 50=> a = 10`
So, Rakesh answered `10` questions correctly and `6` questions incorrectly.

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