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In a certain village, 22% of the families own agricultural land, 18% own a mobile phone and 1600 families own both agricultural land and a mobile phone. If 68% of the families neither own agricultural land nor a mobile phone, then the total number of families living in the village is

  1. 20000
  2. 10000
  3. 8000
  4. 5000

Solution

Let total number of families in the village = x

Number of families own agricultural land, n(A) = 0.22x

Number of families own mobile phone, n(M) = 0.18x

Number of families own both agricultural land and mobile phone, n(A ⋂ M) = 1600

Number of families own agricultural land or mobile phone, n(A ⋃ M) = x - 0.68x = 0.32x

n(A ⋃ M) = n(A) + n(M) - n(A ⋂ M)

n(A ⋂ M) = 0.08x

0.08x = 1600

⇒ x = 20000

The correct option is A.