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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?
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Verified Answer
We have, $\quad n(\mathrm{~T})=150, n(\mathrm{C})=225$
and $n(\mathrm{~T} \cap \mathrm{C})=100$
We know that
$\begin{aligned}
n(T \cup C) &=n(T)+n(C)-n(T \cap C) \\
&=150+225-100=275
\end{aligned}$
Total no. of students $=600$
No. of students who neither take tea nor coffee
$=600-n(\mathrm{~T} \cup \mathrm{C})=600-275=325$
and $n(\mathrm{~T} \cap \mathrm{C})=100$
We know that
$\begin{aligned}
n(T \cup C) &=n(T)+n(C)-n(T \cap C) \\
&=150+225-100=275
\end{aligned}$
Total no. of students $=600$
No. of students who neither take tea nor coffee
$=600-n(\mathrm{~T} \cup \mathrm{C})=600-275=325$
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