9. In a class test (+5) marks are given for every correct answer and (-3) marks are given for
every incorrect answer and no marks for not attempting any question.
(1) Radhika scored 14 marks. If she has got 4 correct answers, how many questions has she
attempted incorrectly?
(ii) Mohini scores -5 marks in this test, though she has got 2 correct answers. How many
questions has she attempted incorrectly?
(iii) Rakesh scores 23 marks by attempting 19 questions. How many questions has he
attempted correctly and how many has he attempted incorrectly?
Answers
Answer:
1) Incorrectly attempted= 3 questions
2)Incorrectly attempted= 5 questions
3) Correctly attempted=10 questions
Incorrectly attempted= 9 questions
Step-by-step explanation:
1) total marks=14
correct answer=4
Marks for correct answer= 5*4=20
Marks for incorrect answer= -3
Incorrect answer= -(total marks -Marks for correct answer)/3
=14-20/3
=-6/-3
=2
2) total marks=-5
correct answer=2
Marks for correct answer= 2*5=10
Marks for incorrect answer= -3
Incorrect answer= -(total marks -Marks for correct answer)/3
=-(-5-10)/3
=-(-15)/3
=15/3
=5
3) total marks= 23
correctly attempted= x
Marks for correct answer= x*5=5x
incorrectly atempted=y
Marks for incorrect answer= -3y
total questions=19
x+y=19-----equation 1
5x+5y= 95-------equation 2
5x+5y= 95
-(5x-3y=23)
8y=72
y=9
Substituing the value of y in in equation 1
x+y=19
x+9=19
x=19-9
x=10
correctly attempted= x=10
incorrectly attempted=y=9
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( i ) -- Radhika has attempted 2 questions incorrectly.
( ii ) -- Mohini has attempted 5 questions incorrectly.
( iii ) 10 questions have been attempted correctly and 9 questions have been attempted incorrectly.
SOLUTION --
( i ) Marks scored by radhika = 14
Marks obtained for 4 correct answer = 4 × 5 = 20
Marks obtained for incorrect answer
= Total score - Marks obtained for 4 correct answers
= 14 - 20 = -6
Marks obtained for 1 wrong answer = -3
Thus number of incorrect answes = -6/-3 = 2
( ii ) Marks scored by mohini = -5
Marks obtained for 2 correct answer = 2 × 5 = 10
Marks obtained for incorrect answer
= Total score - Marks obtained for 2 correct answers
= -5 - 20 = -15
Marks obtained for 1 wrong answer = -3
Thus number of incorrect answes = -15/-3 = 5
( iii ) Let X be number of correct and Y be number of wrong answers. Then,
X + Y = 19
5X - 3Y = 23
Y = 19 - X
5X - 3( 19 - X ) = 23
5X - 57 + 3X = 23
5X + 3X = 23 + 57
8X = 80
X = 80/8
X = 10
Y = 19 - 10 = 9
