In a competitive examination, one mark is awarded for each correct answer while 1/2 mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?
NCERT Class X
Mathematics - Exemplar Problems
Chapter _PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

1
answer is 100.
No it's 60

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2015-07-20T07:37:26+05:30

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Total answers = 120
Let the number of correct answers = x
number of wrong answers = (120-x)

Marks awarded for each right answer = 1
then Marks awarded for x right answer = x × 1 = x marks
Marks deducted for each wrong answer = 0.5
then marks deducted for (120-x) right answers = (120-x) × 0.5 = 60 - 0.5x

So she will get= marks awarded for right answer - marks deducted for wrong answer
                     = x - (60-0.5x)
                     = x - 60 + 0.5x
                     = 1.5x - 60
And she has got = 90 marks
So

1.5x - 60 = 90
⇒ 1.5x = 90 + 60
⇒ 1.5x = 150
⇒ x = 150/1.5 
⇒ x = 100

So she did 100 questions correctly.
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