Question

In a group of $70$ students, $40$ like only cricket, $15$ like both cricket and badminton, then the number of students who like badminton is

• A. $15$
• B. $25$
• C. $40$
• D. $30$

Answer 1

The correct option is D $30$

Given a group of $70$ students.
$40$ like only cricket and $15$ like both cricket and badminton
Let, $A$ is the group of students who like cricket,
$B$ is the set of people who play badminton.
$\Rightarrow n(A\cup B)=70;n(A-B)=40;n(A\cap B)=15$
$\Rightarrow n\left(A\right)=n(A-B)+n(A\cap B)=40+15=55$
Now, we know the formula:
$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$
$\Rightarrow 70=55+n\left(B\right)-15$
$\Rightarrow n\left(B\right)=70-55+15=30$
Thus, the number of people who like badminton is $30.$