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Question

# There are 90 multiple choice questions in a test. Two marks are awarded for every correct answer and one mark is deducted for every wrong answer. If Sahana got 60 marks in the test while she answered all the questions, then how many questions did she answer correctly?

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Solution

## Suppose the number of correctly answered questions be 'x', then number of wrongly answer questions =90−xIt is given that for every correct answer 2 marks are awarded.∴ Number of marks scored for correct answers =2xAnd it is given that for every wrongly answered questions '1' mark is deducted∴ Number of marks to be deducted from the score=(90−x)×1=90−xTotal score 2x−(90−x)=2x=90+x=3x−90But it is given that total score is 60⇒ 3x−90=603x=60+903x=150x=1503=50Number of questions answered correctly =x=50

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