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 minimum number of people who could have named all three places as their favourite.

• A. 25
• B. 50
• C. 60
• D. 35

Answer 1

The correct option is B 50

For III to be the minimum, II has to be the maximum.

also, all the equations will have to be satisfied.

We have II +2III = 150

Also I + II + III = 100.

II can take a maximum value of 50. So, III = 50, at this point all the equations are consistent, hence 50 is the minimum number of people.