Question

In a group of 50 people who like either coffee or tea, 15 like coffee but not tea and 32 like coffee. How many like tea alone?

• A. 18
• B. 17
• C. 30
• D. 35

Answer 1

The correct option is A

18

Let $U$ be the universal set, and sets $C$ and $T$ represent the sets of people who like coffee and tea respectively. Then, the given situation is represented by the Venn diagram given below.

Since everyone likes at least coffee or tea, $n\left(U\right)=n(C\cup T)=50.$
Also, given that $n\left(C\right)=32.$

$n\left(\text{only coffee}\right)=n(C-T)=15$

$n(C\cap T)=n\left(C\right)-n(C-T)=32–15=17$

But, $n(C\cup T)=n\left(C\right)+n\left(T\right)–n(C\cap T).$

$\Rightarrow 50=32+n\left(T\right)-17$

$\Rightarrow n\left(T\right)=35$

$\text{Now,}n\left(\text{only tea}\right)=n(T-C)=n\left(T\right)-n(C\cap T).$

$\Rightarrow n(T-C)=35–17=18$