Question

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 cofee and tea?

Answer 1

Step 1:
Given data: Let $C$ denote the set of people who like coffee and $T$ denote the set of people who like tea.
Number of people who like coffee $=n\left(C\right)=37$
Number of peole who like tea $=n\left(T\right)=52$
Number of people who like at least tea or coffee $=n(C\cup T)=70$

Step 2: Solve for $n(C\cap T)$
We know that,
$n(C\cup T)=n\left(C\right)+n\left(T\right)-n(C\cap T)$
$\Rightarrow 70=37+52-n(C\cap T)$
$\Rightarrow 70=89-n(C\cap T)$
$\Rightarrow n(C\cap T)=19$

Final answer:
Number of people who like both coffee and tea is $19$