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In a competitive examination, 1 mark is ...

In a competitive examination, 1 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?

Text Solution

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Let the number of questions attempted correctly = x
Number of questions answered = 120
So, wrong answer attempted = 120 - x
Marks awarded for right answer = 1 `xx` x = x marks
Marks deducted for (120 - x) wrong answer = `(1)/(2)` (120 - x)
To marks awarded = 90
`therefore " "x- (1)/(2) (120 - x) = 90 " implies "x - 60 + (x)/(2) = 90`
`implies " "x + (x)/(2) = 90 + 60 " "implies " "(3x)/(2) = 150`
`implies " "x = (150 xx 2)/(3) " "implies" "x = 100`
Hence, Jayanti answered 100 questions correctly.
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