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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
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B
6
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C
7
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D
8
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Solution

The correct option is D 8
Let n(G)= tourists who liked Goa
n(K)= tourists who liked Kerala
n(B)= tourists who liked Bangalore
n(GKB)=n(G)+n(K)+n(B)n(GK) n(KB)n(BG)+n(GKB)

86=40+30+305107+n(GKB)
n(GKB)=8

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