In a town of 10000 families, it was found that 40% families buy newspaper A, 20% families buy newspaper B, 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 newspaper. Find
(i) the number of families which buy newspaper A only.
(ii) the number of families which buy none of A , B and C.

Options

A. 3100
B. 3300
C. 2900
D. 1400

Answer

B

Explanation

n( A) = 40 % of 10,000=4000
n(B) = 20 % of 10,000 =2 ,000
n( C) = 10 % of 10,000 = 1000
`n( A cap B)= 5% of 10,000 =500 `
`n(B cap C)= 3% of 10,000 = 300 `
`n(C cap A) = 4% of 10,000 = 400`
`n(A cap B cap C ) = 2% of 10,000 = 200 `
Number of families which buy newpaper A only
`n( A cap B^c cap C^c)`
` n[A cap (B cup C)^c]`
`=n (A) -n[(A cap B )cup n(A cap C)]`
`n(A)-[n(A cap B)+n(A cap C ) -n (A cap B cap C)]`
= 4000-[500 + 400-200]
= 4000 - 700
= 3300