Question

In a group of $65$ people, $40$ like cricekt, $10$ like both cricket and tennis. If every person likes atleast one of the two games. then choose the correct option.

• A. $30$ people like tennis
• B. $35$ people like tennis
• C. $30$ people like only tennis
• D. $25$ people like only tennis

Answer 1

Answer: (B), (D)

$25$ people like only tennis

Let $C$ is the set of people who like cricket.
$\Rightarrow n\left(C\right)=40$
$T$ is the group who like tennis
$\Rightarrow n(C\cap T)=10$
Also, $n(C\cup T)=65$
Now, using the formula:
$n(C\cup T)=n\left(C\right)+n\left(T\right)-n(C\cap T)$
$\Rightarrow 65=40+n\left(T\right)-10$
$\Rightarrow n\left(T\right)=65-40+10=35$
Hence, $35$ people like tennis.
Now, $n(T-C)=n\left(T\right)-n(C\cap T)=35-10=25$
Hence, $25$ like only tennis.