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?

• A. $310$
• B. $320$
• C. $327$
• D. $325$

Answer 1

Answer: (D)

Let $C$ and $T$ denote the number of students taking coffee and tea, respectively.
Here, $n(T)=150$, $n(C)=225$, $n(C\cap T)=100$
We know that
$n(C\cup T)=n(T)+n(C)-n(C\cap T)$
$\Rightarrow n(C\cup T)=150+225-100$
$\Rightarrow n(C\cup T)=275$
Given, total number of students $=600=n(U)$
We have to find the number of students taking neither tea nor coffee i.e., $n(C\cup T{)}^{\prime }$.
$\therefore n(C\cup T{)}^{\prime }=n(U)-n(C\cup T)$
$=600-275=325$