Question

In a group, if 60% of people drink tea and 70% drink coffee. What is the maximum possible percentage of people drinking either tea or coffee but not both?
A) 100%
B) 70%
C) 30%
D) 10%

Answer 1

Hint: First thing to note is that no information is mentioned about the people who don’t like either of them, consider what "Nobody doesn’t drink"
Now everyone in the group either drinks one of the drinks or both. So we have three kinds of people.
People who drink tea
People who drink coffee
People who drink both tea and coffee
and then see how big each of those groups are.

Complete step-by-step answer:
To find maximum possible percentage of people drinking either coffee or tea, we can assume everyone drinks at least either of the options.
Hence
\[a + b = 100\]
\[60 + 70 = 130\]
\[Both = 130 - 100 = 30\]
Tea drinkers left $ = 60 - 30 = 30\% $
Coffee drinkers left $ = 70 - 30 = 40\% $
Maximum possible percentage of people drinking either tea or coffee but not both\[ = {\text{ }}30\% + 40\% = 70\% \]

The reason behind this is pretty straight forward. If you consider a total of 100 individuals, 70 of them like coffee. The remaining 30 don’t like coffee. Let us assume that all 30 of these like tea but we still need 30 more people to like tea. Where are those 30 going to come from? They are going to come from the coffee drinkers because there is no one else left. The surplus of 30 needs to be adjusted inside the coffee drinkers. That is the reason that 30% of people like both Tea and Coffee.

So, option (B) is the correct answer.

Note: For Maximum and Minimum of values, the key point to note is:
If you allot a value to the intersection, it will get added to all the individual sets but will bring down the total. If we want to minimize those who like both, we have to minimize the value in the intersection. So, we have to maximize the value of the union.