Question

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.

Answer 1

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