Question

Question 21
In a competitive examination, 1 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?
Assume she answered all the questions.

Answer 1

Let $x$ be the number of correct answers of the questions in a competitive examination, then (120 – x) will be the number of wrong answers of the questions.
Then, by given conditions,
$(x\times 1)-\left(\right(120-x)\times \frac{1}{2})=90$
$\Rightarrow$ $\frac{3x}{2}$ - 60 = 90
$\Rightarrow \frac{3x}{2}=150\therefore x=\frac{150\times 2}{3}=50\times 2=100$
Hence, Jayanti answered 100 questions correctly.