Question

In a class of $60$ students, if $25$ students play cricket, $20$ students play tennis and $10$ students play both the games, then the number of students who play neither is

• A. $45$
• B. $0$
• C. $25$
• D. $35$

Answer 1

The correct option is C

$25$

Explanation for correct option:

Finding the number of students who play neither:

Let $\mathrm{A}$ be the set of students who are playing cricket and $\mathrm{B}$ be the set of students who are playing tennis, then

$$\begin{gathered} \mathrm{n}\left(\mathrm{A}\right)=25, \\ \mathrm{n}\left(\mathrm{B}\right)=20 \end{gathered}$$

also, $\mathrm{n}\left(\mathrm{AB}\right)=10$ students who play both the games.

Therefore,

$\begin{array}{rcl}\mathrm{n}\left(\mathrm{AUB}\right)& =& \mathrm{n}\left(\mathrm{A}\right)+\mathrm{n}\left(\mathrm{B}\right)-\mathrm{n}\left(\mathrm{AB}\right)\\ & =& 20+25-10\\ & =& 35\end{array}$

Number of students who play neither cricket nor tennis$=60-35$

$=25$

Hence, the correct option is C.