Question

In a party, $70$ guests were to be served tea or coffee after dinner. There were $52$ guests who preferred tea while $37$ preferred coffee. Each of the guests liked one or the other beverage. How many guests liked both tea and coffee?

• A. $15$
• B. $18$
• C. $19$
• D. $33$

Answer 1

The correct option is C $19$

Total number of guests $=70$

Let $A$ and $B$ be the guests who preferred tea and coffee respectively.

$n\left(A\right)=52$

$n\left(B\right)=37$

$n(A\cup B)=70$

$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cup B)$

$=52+37-70=89-70=19$

Guests who liked both tea and cofffee $=19$