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Question

There was a survey conducted in a city about number of people reading newspaper A, B and C. There are 42% of people read newspaper A; 51% of people read newspaper B and 68% of people read paper C. 30% of people read both newspaper A and B. 28% reads B and C and 36% read C and A. 8% do not read any newspaper. Find the percentage of people who read all the three newspapers.


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Solution

Given survey data

n(A) = percentage of people read newspaper A = 42%

n(B) = percentage of people read newspaper B = 51%

n(C) = percentage of people read newspaper C = 68%

n(AB) = percentage of people read newspaper A and B = 30%

n(BC) = percentage of people read newspaper B and C = 28%

n(CA) = percentage of people read newspaper C and A = 36%

since, its given 8% people do not read any newspaper

percentage of people read newspaper = Total people - people don't read newspaper

n(AUBUC) = 100% - 8% = 92%

we know,

n(AUBUC) = n(A) - n(AB) + n(ABC)

92 = 42 + 51 + 68 - 30 - 28 - 36 + n(ABC)

92 = 161 - 94 + n(ABC)

92 = 67 + n(ABC)

n(ABC) = 92 - 67 = 25%

Percentage of people who read all the three newspapers = 25%


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n(A∪B∪C) = n(A) + n(B) + n(C) − n(A∩B) − n(B∩C) − n(C∩A) + n(A∩B∩C)
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