Indian Institute of Foreign Trade 2015 Solved Paper

Question : 9 of 124

Marks: +1, -0

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:

20000
10000
8000
5000

Validate

Solution:

(a) Number of families own agricultural land n (A) = 22%
Number of families own mobile phone n(B) = 18%
Number of families own mobile phone and agricultural land n(A

∩

B) = 1600
Now, Number of families own either agricultural land or a mobile phone

n ( { \A } ∪ { \B } ) = 100 - 68 = 32 \%

∴ ( { \A } ∪ { \B } ) = n ( { \A } ) + n ( { \B } ) - n ( { \A } ∩ { \B } )

32 = 22 + 18 - { n } ( { \A } ∩ { \B } )

⇒ { n } ( { \A } ∩ { B } ) = 8 \%

So, Total number of families = 20,000

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