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 , how many of her questions were right?

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Solution

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 $2 x$ . 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)

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

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