Question

In a community it is found that $52$% people like coffee and $73$% like tea. If $x\%$ like both coffee and tea then

• A. $x\ge 25$
• B. $x\le 52$
• C. $25\le x\le 52$
• D. all of these

Answer 1

Answer: (C)

$25\le x\le 52$

Let $A=$ number of people like coffee, $B=$ number of people like tea.

$\therefore n\left(A\right)=52$% $n\left(B\right)=73$%

$n(A\cap B)=x$%

Let total people in the community =$100=n\left(U\right)$

$\therefore n(A\cup B)\le 100$

$n\left(A\right)+n\left(B\right)-n(A\cap B)\le 100$

$52+73-x\le 100$

$\Rightarrow 125-x\le 100$

$\Rightarrow \therefore x\ge 25$...(i)

Again $A\cap B\subseteq A$

$\Rightarrow n(A\cap B)\le n\left(A\right)$

$x\le 52$ ...(ii)

$\therefore$ By (i) and (ii)$25\le x\le 52$