Question

In a class of $100$ students, $55$ students have passed in physics and $67$ students have passed in Mathematics. Find the number of students passed in Physics only.

Answer 1

Solution:

Let $M$ and $P$ be the sets of the students who passed Mathematics and Physics respectively.

Here,

$n\left(U\right)=100$

$n\left(M\right)=67$

$n\left(P\right)=55$

Since, all students have passed $n\left(U\right)=n(M\cup P)=100$

Now,

$n(M\cup P)=n\left(M\right)+n\left(P\right)-n(M\cap P)$

or, $100=67+55-n(M\cap P)$

or, $n(M\cap P)=122-100=22$

Now, set of students who only passed in Physics denoted by $n_{\circ }\left(P\right)=n\left(P\right)-n(M\cap P)$

$n_{\circ }\left(P\right)=55-22=33$

Therefore, number of students passed in Physics only $=33.$