Question

In a group of 70 people, 37 like coffee, 52 like tea and each person like at least one of the two drinks. The number of persons liking both coffee and tea is ___.

• A. 16
• B. 13
• C. 19
• D. 20

Answer 1

The correct option is C

19

Let the sets $C$ and $T$ represent the sets of people who like coffee and tea respectively.
Let $x$ be the number of people who like both coffee and tea.
THen, $x=n(C\cap T).$
Then, the below given Venn diagram represents the given situation:

As each person in the group likes at least one drink,
$n(C\cup T)=n\left(U\right)=70.$

$\text{But,}n(C\cup T)=n\left(C\right)+n\left(T\right)-n(C\cap T).$

$\Rightarrow 70=37+52-x$

$\Rightarrow x=n(C\cap T)=19$.