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

Answer:

Here, we are given positive marks for every correct answer and negative marks for every incorrect answer i.e. for the correct answer =+3 and for every incorrect answer =−2 mark.

(i)

Radhika got total marks =20, the correct answer =12

So, the total marks for correct answer = marks for correct answer × number of correct answers.

⇒ Total marks for correct answer =3×12 marks

Multiply the terms,

⇒ Total marks for correct answer =36 marks

Thus, Radhika got a total of 36 marks for 12 correct answers.

Now, subtracting the total marks of the correct answer from the total marks we will get marks for incorrect answers. So, writing as

⇒ Total marks for incorrect answer =20−36 marks

Subtract the values,

⇒ Total marks for incorrect answer =−16 marks

So, she got 16 marks for the incorrect answer. Now, we know that for every incorrect answer =−2 marks.

So, the total marks for incorrect answers = marks for incorrect answer × number of incorrect answers.

Substituting values, we get

⇒−16=−2× number of incorrect answers

So, dividing by −2 on both sides, we get

⇒ Number of incorrect answers =8

Hence, the number of incorrect answers is 8.

(ii)

Mohini got total marks =−5, the correct answer =7

So, the total marks for correct answer = marks for correct answer × number of correct answers.

⇒ Total marks for correct answer =3×7 marks

Multiply the terms,

⇒ Total marks for correct answer =21 marks

Thus, Radhika got a total of 21 marks for 7 correct answers.

Now, subtracting the total marks of the correct answer from the total marks we will get marks for incorrect answer. So, writing as

⇒ Total marks for incorrect answer =−5−21 marks

Subtract the values,

⇒ Total marks for incorrect answer =−26 marks

So, she got 26 marks for the incorrect answer. Now, we know that for every incorrect answer =−2 marks.

So, the total marks for incorrect answers = marks for incorrect answer × number of incorrect answers.

Substituting values, we get

⇒−26=−2× number of incorrect answers

So, dividing by −2 on both sides, we get

⇒ Number of incorrect answers =13

Hence, the number of incorrect answers is 13.