Question:
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?
Solution:
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,
$x \times 1-(120-x) \times \frac{1}{2}=90$
$\Rightarrow$ $x-60+\frac{x}{2}=90$
$\Rightarrow$ $\frac{3 x}{2}=150$
$\therefore$ $x=\frac{150 \times 2}{3}=50 \times 2=100$
Hence, Jayanti answered correctly 100 questions.