12. In a test (+5) marks are given for every correct answer and (–2) marks are given for every incorrect answer.
(i) Saina answered all the questions and scored 30 marks though she got 10 correct answers.
(ii) Hemant also answered all the questions and scored (–12) marks though he got 4 correct answers. How many
incorrect answers had they attempted?
Answers
Given :-
In a test (+5) marks are given for every correct answer and (–2) marks are given for every incorrect answer.
(i) Saina answered all the questions and scored 30 marks though she got 10 correct answers.
(ii) Hemant also answered all the questions and scored (–12) marks though he got 4 correct answers.
To Find :-
Incorrect answers
Solution :-
For sania
Let the incorrect answer be x
Correct marks + Incorrect marks = 30
5(10) + (-2)(x) = 30
50 + (-2x) = 30
50 - 2x = 30
-2x = 30 - 50
-2x = -20
2x = 20
x = 20/2
x = 10
For Hemant
Let the incorrect answer be x
5(4) + (-2)(x) = -12
20 - 2x = -12
-2x = -12 - 20
-2x = -32
x = -32/-2
x = 16
[tex][/tex]
Given:
Marks given for every correct answer = 5
Marks deducted for every wrong answer = 2
Question:
(i) Saina answered all the questions and scored 30 marks though she got 10 correct
answers.
How many incorrect answers had she attempted?
Solution:
Correct answers = 10
Total marks scored = 30
If, marks scored for correct answers = 10×5 = 50
then 20 marks is lost for wrong answer.
So, 20/2 = 10, Therefore she gave 10 answers wrong.
Total questions answered by Saina = 10 + 10 = 20
Therefore,
Incorrect answers attempted by Saina = 10
Question:
(ii) Hemant also answered all the questions and scored (-12) marks though he got 4 correct
answers.
How many incorrect answers had he attempted?
Solution:
Correct answers = 4
Total marks scored = -12
If, marks scored for correct answers = 4×5 = 20
then 32 marks is lost for wrong answer.
So, 32/2 = 16, Therefore he gave 16 answers wrong.
Total questions answered by Hemant = 4 + 16 = 20
Therefore,
Incorrect answers attempted by Hemant = 16