In a town 10,000 families it was found that 40% families buy newspaper A, 20% families buy newspaper B and 10% families buy newspaper C. 5% families buy A and B, 3% buy B and C and 4% buy A and C. If 2% families buy all the three newspapers, find the number of families which buy A only.

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3300

3500

3600

3700

answer is A.

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Detailed Solution

Given,
Total families = 10000
40% families buy newspaper A,

n (A) = 40 % of 10, 000 = 4, 000

20% families buy newspaper B,

n (B) = 20 % of 10, 000 = 2, 000

10% families buy newspaper C

,

n (C) = 10 % of 10, 000 = 1, 000

5% families buy A and B,

n (A \cap B) = 5 % of 10, 000 = 500

3% families buy B and C,

n (B \cap C) = 3 % of 10, 000 = 300

4% families buy A and C.

n (C \cap A) = 4 % of 10, 000 = 400

Only 2% families buy all the three newspapers

,

n (A \cap B \cap C) = 2 % of 10, 000 = 200

So, the families which only buy newspaper A,

n (A only) = n (A) - [n (A \cap B) + n (A \cap C)] + n (A \cap B \cap C)

n (A only) = 4000 - [500 + 400] + 200 = 4000 - 700

n (A only) = 3300

option 1 is correct.

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