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?
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?
Let $C$ denote the set of people who like coffee, and $T$ denote the set of people who like tea
$n(C \cup T)=70, n(C)=37, n(T)=52$
We know that:
$n(C \cup T)=n(C)+n(T)-n(C \cap T)$
$\therefore 70=37+52-n(C \cap T)$
$\Rightarrow 70=89-n(C \cap T)$
$\Rightarrow(C \cap T)=89-70=19$
Thus, $19$ people like both coffee and tea.
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