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

Given data:
Let $T,C$ be the set of students taking tea and coffee respectively.
Number of students taking tea $=n\left(T\right)=150$
Number of students taking coffee $=\left(C\right)=225$
Number of students taking both tea and coffee $=n(T\cap C)=100$

Solve for students taking either tea or coffee.
$n(T\cup C)=n\left(T\right)+n\left(C\right)-n(T\cap C)$
$=150+225-100=275$

Step 3: Solve for number of students taking neither tea nor coffee.
Number of students taking neither tea nor coffee.
=Total number of students - Number of students who like either tea or coffee
$=600-275$
$=325$

Final answer:
Hence, $325$ students were taking neither tea nor coffee.