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., $n(C \cup T)'$.
$\therefore n (C \cup T)' = n(U) - n (C \cup T)$
$ = 600 - 275 = 325$