Question

In a group of 70 people, 37 like coffee, 52 like tea and each person likes atleast one of the two drinks. The number of people who like both coffee and tea, is ...X... . Here, $X$ refers to

• A. 89
• B. 55
• C. 85
• D. 19

Answer 1

Answer: (D)

Let $A$ be the set who like coffee and $B$ be the set who like tea.
Then, $n(A\cup B)=70,n(A)=37$ and $n(B)=52$
$n(A\cup B)=n(A)+n(B)-n(A\cap B)$
$70=37+52-n(A\cap B)$
$n(A\cap B)=19$
Thus, 19 people like both coffee and tea.