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Let the number of people who had all 3 drinks be x. Number of people who had - Only tea & coffee = 40 - x - Only coffee & milk = 50 - x - Only milk & tea = 55 - x Number of people who had - Only Tea = 120−(40−x+55−x+x) = x + 25 - Only Coffee =100−(40−x+50−x+x) = x + 10 - Only Milk =90−(50−x+55−x+x) = x - 15 |
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Case I: None of the 7 regions can be negative. The numbers x−15 and 40−x set the minimum and maximum values for x. x−15>0 ⇒ x>15 40−x>0 ⇒ x<40 ∴ Minimum and maximum number of people who had all 3 drinks is 15 and 40 respectively. |
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