Out of 100 persons 50 drink Pepsi, 40 drink Coke and 20 drink both Pepsi and
Coke. The number of persons who neither drink Pepsi nor Coke is ___.



Set P, which is composed of regions "a" and "b", contains as 
elements all 50 people who drink Pepsi.

Set C, which is composed of regions "b" and "c", contains as 
elements all 40 people who drink Coke.  

We first look at this sentence:

>> 20 drink both pepsi and coke <<

That means there are 20 people in the overlapping part of the two 
circles, which is the region labeled "b".

So we put 20 instead of "b":



We see the words:

>>50 drink pepsi<<

We have already accounted for 20 of the 50, so the remaining 50-20 or 30
are in the region of set A labeled "a", so we put 30 where the "a" is:



Then we see the words:

>>40 drink Coke<<

We have already accounted for 20 of the 40, so the remaining 40-20 or 20
are in the region of set B labeled "c", so we put 20 where the "c" is:



Finally we see the words:

>>100 persons<<

We have already accounted for the number of elements of the three 
regions in the circles. So we add what we have 30+20+20=70 so the 
remaining 100-70=30 must be in the region outside both circles 
but inside the rectangle, which is the universal set, so we put 
30 in the outer region labeled "d": 

 

So the answer is 30.

Edwin