Question

There was a survey 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 read all the three newspaper.

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Answer 1

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(A $\cap$ B) = percentage of people read newspaper A and B = 30%

n(B $\cap$ C) = percentage of people read newspaper B and C = 28%

n(C $\cap$ A) = 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(A $\cup$ B $\cup$ C) = 100% - 8% = 92%

we know,

n(A $\cup$ B $\cup$ C) = ∑ n(A) - ∑ n(A $\cap$ B) + n(A $\cap$ B $\cap$ C)

92 = 42 + 51 + 68 - 30 - 28 - 36 + n(A $\cap$ B $\cap$ C)

92 = 161 - 94 + n(A$\cap$ B $\cap$ C)

92 = 67 + n(A $\cap$ B $\cap$ C)

n(A $\cap$ B $\cap$ C) = 92 - 67 = 25%

Percentage of people read all the three newspaper = 25%