Question

In a quiz program,the correct answer gets you $2$ marks. For each wrong answer, one mark is deducted from the total score. There are $50$ questions to be answered. If Preeti scored $76$ marks for the quiz, how many of her questions were right?

• A. $26$
• B. $13$
• C. $42$
• D. $38$

Answer 1

The correct option is C $42$

As the number of questions answered is unknown, let us assume that unknown variable as '$x$'.
If the number of questions answered correctly are x, then the number of questions answered incorrectly will be $(50-x)$.
For each correct answer, she gets $2$ marks. So the marks scored for x correctly answered questions are $2x$. Similarly, the marks deducted for (50-x) incorrectly answered questions are $(50-x)\times 1=50-x$
Now, the total marks scored by Preeti will be
$\text{2x- (50 -x) = 2x -50 +x = 3x -50}$ (For each wrong answer, one mark is deducted from the total score)

$\text{The final equation is, 3x -50 = 76}$
$\text{3x = 50 +76 = 126}$
$x=\frac{126}{3}=42$
$\text{So, the total number of questions answered correctly by Preeti are 42.}$