Question

There are $90$ multiple choice questions in a test. Two marks are awarded for every correct answer and one mark is deducted for every wrong answer.

If Sahana got $60$ marks in the test while she answered all the questions, then how many questions did she answer correctly?

Answer 1

Suppose the number of correctly answered questions be '$x$', then number of wrongly answer questions $=90-x$
It is given that for every correct answer $2$ marks are awarded.
$\therefore$ Number of marks scored for correct answers $=2x$
And it is given that for every wrongly answered questions '$1$' mark is deducted
$\therefore$ Number of marks to be deducted from the score
$=(90-x)\times 1=90-x$
Total score $2x-(90-x)=2x=90+x=3x-90$
But it is given that total score is $60$
$\Rightarrow$ $3x-90=60$
$3x=60+90$
$3x=150$
$x=\frac{150}{3}=50$
Number of questions answered correctly $=x=50$