In a competitive examination, one mark is awarded for each correc… - Vidyadip

Question

In a competitive examination, one mark is awarded for each correct answer while $\frac{1}{2}$ mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?

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Answer

Let x be the number of correct answers of the questions in a competitive examination, then (120 - x) be the number of wrong answers of the questions.
Then, by given condition,
$\text{x}\times1-(120-\text{x})\times\frac{1}{2}=90$
$\Rightarrow\ \text{x}-60+\frac{\text{x}}{2}=90$
$\Rightarrow\ \frac{3\text{x}}{2}=150$
$\therefore\ \text{x}=\frac{150\times2}{3}=50\times2=100$
Hence, jayanti answered correctly 100 questions.

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