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?

• A. $70$
• B. $125$
• C. $66$
• D. $100$

Answer 1

The correct option is D $100$

Let $x$ be the number of correct answers and $y$ be the number of wrong answers.

Since Jayanti answered $120$ questions therefore, $x+y=120$ that is

$x=120-y..........\left(1\right)$

Also, it is given that one mark is awarded for each correct answer while $\frac{1}{2}$ mark is deducted for every wrong answer and Jayanti got $90$ marks, therefore,

$x-0.5y=\mathrm{90..........}\left(2\right)$

Substituting the value of equation 1 in equation 2:

$120-y-0.5y=90$

$-1.5y=-30$

$y=20$

Therefore,

$x=120-20=100$

Hence, she answered $100$ questions correctly.