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 $A$ deontes the set of people who likes coffee and $B$ denotes the set of people who likes tea .
then, it is given that $n\left(A\right)=37,n\left(B\right)=52\text{and}n(A\cup B)=70$

$\text{Using}n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$

$\Rightarrow 70=37+52-n(A\cap B)$
$\Rightarrow n(A\cap B)=19$.