Question

In a class of $35$ students, $26$ students like to eat apples and $16$ students like to eat oranges. Also ,each student likes to eat at least one of the two fruits. How many student like to eat both the fruits?

Answer 1

Total number of student in the class = $35$

Number of students like to eat apples $n\left(A\right)=26$

Number of students like to eat oranges $n\left(O\right)=16$

Number of students who like at least one fruit $n(A\cup O)=35$

Number of students who like both $n(A\cap O)==?$

we know that,

$n(A\cup O)=n\left(A\right)+n\left(O\right)-n(A\cap O)$

$\Rightarrow 35=26+16-n(A\cap O)$

$\Rightarrow n(A\cap O)=42-35$

$\Rightarrow n(A\cap O)=7$

Hence, total number of students like both oranges and apple is $7$