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Question

In a competitive examination , one mark is awarded for each correct answer while 1/2 mark is deducted for everey wrong answer . Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly.

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Solution

Let the number of correct answers be x and the number of wrong answers be y.
Total questions Jayanthi answered = 120
So, x + y = 120 .....(i)
Now, marks obtained for answering correctly = 1 × x = x
Marks deducted for answering incorrectly = 1/2×y = y/2
Total marks obtained = x-y/2=90 .....(ii)
Subtracting (ii) from (i), we get
y+(y/2)=30⇒3y/2=30⇒y=20
Putting y = 20 in (i), we get
x + 20 = 120
⇒ x = 100
Thus, Jayanti answered 100 questions correctly.


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