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In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?
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Verified Answer
Let $C=$ Set of people who like coffee and $T=$ Set of people who like tea.
Then, $n(C \cup T)=70, n(C)=37$.
$n(T)=52, n(C \cap T)=\text { ? }$
Now, we know that
$\begin{aligned}
& n(C \cup T)=n(C)+n(T)-n(C \cap T) \\
\Rightarrow & 70=37+52-n(C \cap T) \\
\Rightarrow & n(C \cap T)=89-70=19
\end{aligned}$
Hence, 19 people like both coffee and tea.
Then, $n(C \cup T)=70, n(C)=37$.
$n(T)=52, n(C \cap T)=\text { ? }$
Now, we know that
$\begin{aligned}
& n(C \cup T)=n(C)+n(T)-n(C \cap T) \\
\Rightarrow & 70=37+52-n(C \cap T) \\
\Rightarrow & n(C \cap T)=89-70=19
\end{aligned}$
Hence, 19 people like both coffee and tea.
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