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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−x

It is given that for every correct answer 2 marks are awarded.

∴ Number of marks scored for correct answers =2x

And 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−x

Total score 2x−(90−x)=2x=90+x=3x−90

But it is given that total score is 60

⇒ 3x−90=60

3x=60+90

3x=150

x=1503=50

Number of questions answered correctly =x=50

It is given that for every correct answer 2 marks are awarded.

∴ Number of marks scored for correct answers =2x

And 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−x

Total score 2x−(90−x)=2x=90+x=3x−90

But it is given that total score is 60

⇒ 3x−90=60

3x=60+90

3x=150

x=1503=50

Number of questions answered correctly =x=50

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