In a group of 100 persons 60 like bananas,75 like apples .if x persons like both banana and apple then show that xlies between 30 and 60.
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Now, the group is of 100 people , so for the max value of x we take the case as,
1) Out of the survey there were 25 people who did not like either banana or apple (25 because (100- 75) , 75 people like apples)
So,
n(a)=60
n(b)=75
n(a∪b)=75
So,
n(a∩b)= 75 +60- 75
n(a∩b) =60
So, max value could be 60
For the min value,
Let us consider all 100 people took the survey and liked either an apple or banana
So,
n(a)=60
n(b)=75
n(a∪b)=100
n(a∩b)= 60+ 75 -100
n(a∩b)= 35
So,
the value of x will lie between 35 to 60
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