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Question

In a survey, 100 people were asked about their favourite Holiday spot in India among three places: Goa, Shimla or Kashmir. All the people had at least one of these three spots as their favourite one. 90 people named Goa as their favourite, 80 people named Shimla as their favourite and 80 people named Kashmir as their favourite.
Determine the maximum number of people who could have name exactly two places as their favourite.


Your Answer
A
40
Correct Answer
B
50
Your Answer
C
60
Your Answer
D
70

Solution

The correct option is B 50

For II to be maximum, III has to minimum i.e. 0. In this case, II = 150. But, II can’t be 150 as the maximum possible value in only 100.

Also,

We have II +2III = 150

Also I + II + III = 100.

So when III=50 and II =50 then all the equations are getting satisfied, hence II=50 is the minimum and maximum value for II

So, maximum value of II = 50

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