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Instructions

A survey of 200 people in a community who watched at least one of the three channels — BBC, CNN and DD — showed that 80% of the people watched DD, 22% watched BBC, and 15% watched CNN.

Question 52

What is the maximum percentage of people who can watch all the three channels?

Solution

Let a be the number who watch only one channel, b be the number who watch only 2 channels and c be the number who watch all channels.

a+b+c = 100

a+2b+3c = 80+22+15 =117

Subtracting both equations,

b+2c = 117-100 = 17

Maximum c occurs when b = 0

2c = 17

c = 8.5

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