Question

In a group of $100$ persons $85$ take tea $20$ take coffee and $25$ take both tea and coffee Number of persons who take neither tea nor coffee is

• A. $5$
• B. $15$
• C. $25$
• D. $20$

Answer 1

Answer: (D)

$20$

Given,

$U=$ a group there are $100$ persons.

$85$ take tea $\Rightarrow n\left(T\right)=85$
$20$ take coffee $\Rightarrow n\left(C\right)=20$
$25$ take both tea and coffee $\Rightarrow n(T\cap C)=25$
Now,

Number of person who take neither tea or coffee
$n\left(\overline{T\cup C}\right)=n\left(U\right)-\left[n\right(T\cup C\left)\right]=n\left(U\right)-\left[n\right(T)+n(U)-n(T\cap C\left)\right]=100-[85+20-25]=20$