Question

In a group of tourists, $40\%$ liked Goa, $30\%$ liked Kerala and $30\%$ liked Bangalore. $7\%$ liked both Goa and Kerala, $5\%$ liked both Kerala and Bangalore, $10\%$ liked both Bangalore and Goa. If $86\%$ of these liked at least one of the places, then what percentage of people liked all three?

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

The correct option is D $8$

Let $n\left(G\right)=$ tourists who liked Goa
$n\left(K\right)=$ tourists who liked Kerala
$n\left(B\right)=$ tourists who liked Bangalore
$n(G\cup K\cup B)=n\left(G\right)+n\left(K\right)+n\left(B\right)-n(G\cap K)-n(K\cap B)-n(B\cap G)+n(G\cap K\cap B)$

$\Rightarrow 86=40+30+30-5-10-7+n(G\cap K\cap B)$
$\Rightarrow n(G\cap K\cap B)=8$