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:
Explanation:
Let total number of families in the village be T Number of families own agricultural land, n(A) = 0.22T
Number of families own mobile phone, n(M) = 0.18T
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) = T – 0.68T = 0.32T
∴ n(A ⋃ M) = n(A) + n(M) – n(A ⋂ M)
∴ n(A ⋂ M) = 0.08T
0.08T = 1600 ⇒ T = 20000
Hence, option (a).
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