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 like both coffee and tea ?

Answer 1

Let,

n(P) denote the total number of people

n(C) denote the number of people who like coffee and

n(T) denote the number of people who like tea.

Then , n(P) = 70

n(C) = 37

n(T)= 52

We are given that each person likes at least one of the two drinks, i.e., $P=C\cup T$

To find : $n(C\cap T)$

We know$n\left(P\right)=n\left(C\right)+n\left(T\right)-n(C\cap T)$

$\Rightarrow 70=37+52-n(C\cap T)$

$\Rightarrow 70=89-n(C\cap T)$

= $n(C\cap T)$ = 89-70

= 19