Question

In a class of $100$ students, $55$ students have passed in Maths, $67$ passed in Physics. If all the students pass in at least one subject, then the number of students who passed in physics only is

• A. $22$
• B. $33$
• C. $10$
• D. $45$

Answer 1

The correct option is D $45$


$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$
$\Rightarrow 100=67+55-n(A\cap B)$
$\Rightarrow n(A\cap B)=22$
Now, $n\left(\text{only}B\right)=n\left(B\right)-n(A\cap B)=67-22=45$