Question

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

• A. 25
• B. 45
• C. 35
• D. 0

Answer 1

The correct option is A 25

Given:

$n\left(U\right)=60\text{{number of students in the class}}$

$n\left(C\right)=25\text{{number of students play cricket}}$

$n\left(T\right)=20\text{{number of students play tennis}}$

$n(C\cap T)=10\text{{number of students play both}}$

We know
$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$\therefore n(C\cup T)=n\left(C\right)+n\left(T\right)-n(C\cap T)$

$\Rightarrow n(C\cup T)=25+20-10=35$

Number of students who play neither

$=n\left(U\right)-n(C\cup T)=60-35=25$

Hence, option (B) is correct.