Question

In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

Answer 1

Let T be the set of students who like tea and C be the set of students who like coffee.

Here $n\left(T\right)=150,n\left(C\right)=225$

and $n(C\cap T)=100$

We know that

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

= $150+225-100=275$

$\therefore$ Number of students taking either tea or coffee = 275

$\therefore$ Number of students taking neither tea nor coffee = $600-275=325$