Question

9.
In a colony, 275 families buy Tamil newspaper, 150 families buy English newspaper,
45 families buy Hindi newspaper, 125 families buy Tamil and English newspapers, 17
families buy English and Hindi newspapers, 5 families buy Tamil and Hindi newspapers
and 3 families buy all the three newspapers. If each family buy atleast one of these
newspapers then find number of families buy only one newspaper ​

Answer 1

Answer:

185 Families buy only one newspaper.

Step-by-step explanation:

Number of families buy Tamil newspaper= A = 275

Number of families buy English newspaper= B = 150

Number of families buy Hindi newspaper= C = 45

Number of families buy both Tamil and English newspaper= A∩B = 125 i.e. AB = 125-3= 122

Number of families buy both English and Hindi newspaper= B∩C = 17 i.e. BC = 17-3= 14

Number of families buy both Tamil and Hindi newspaper= A∩C = 5 i.e. AC= 5-3=2

Number of families buy all three newspapers= ABC = 3

We have to find the number of families who buy only one newspaper = D. According to the Venn diagram,

n(D)= n(A)+n(B)+n(C)-2*[n(AB)-n(BC)-n(AC)}-3*n(ABC)

      = 275+150+45-2*[122+14+2]-3*3

      = 470-276-9

      = 185

Answer: 185 families buy only one newspaper.