Question

11. In a class test 3 marks were given for each correct answer and 2 marks were deducted for every incorrect answer. No marks were allotted for not attempting any question. (i) Piyush scored 40 marks. If he had 20 correct answers, how many of his answers were wrong? (ii) Rohan scored 6 marks in the test although he had 8 correct answers. How many questions did he attempt incorrectly?​

Answer 1

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.

Note: Linear equations are the equations in which the variables are raised to the power equal to one. The linear equations are classified into different types based on the number of variables in the equation. The different types of linear equations are:

Linear equations in one variable are linear equations that consist of only one variable.

Linear equations in two variables are linear equations which consist of two variables.

Linear equations in three variables are linear equations which consist of three variables.

Plss mark brainliest and thankss

Answer 2

Answer:

piyush= 10

Rohan=9

Step-by-step explanation:

PIYUSH

marks if diduction was never done =3*20=60

but marks obtained=40

It means 20 marks were cut for incorrect answers

So deduction for 1 incorrect answers =2

no of wrong answers=20/2=10

Rohan

marks if deduction was not applied=8*3=24

marks obtained =6

24-6=18

ie wrong answers cancelled 18 marks

Marks cancelled for one wrong is 2

so number of incorrect answers are 18/2=9