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?

Note: Preeti attempted all the 50 questions

• 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 scored for $(50-x)$ incorrectly answered questions are $(50-x)\times 1=50-x$
Now, the total marks scored by Preeti will be
$2x-(50-x)=2x-50+x=3x-50$
[For each wrong answer, one mark is deducted from the total score]

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