Math CentralQuandaries & Queries


Question from Chibo:

In a survey of 60 sport fans, 45 enjoy soccer, 35 enjoy cricket and 10 do not enjoy either soccer or cricket, but some other sports.What percentage of sports fans enjoys both soccer and cricket?


Suppose I have a large room that will hold the 60 fans and I draw two circles on the floor, one for the soccer fans and one for the cricket fans. Some of the people may be fans of both sports so the circles have an overlap.


First I bring in the 10 people who are fans of neither sport and they stand outside the two circles. Then I bring in the remaining fans and have them stand in the appropriate circles. Since 60 - 10 = 50 there are 50 people to arrange in the two circles. But 45 + 35 = 80. How many people are in the overlap of the two circles? What is this as a percentage of 60?


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