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%

To find the maximum percentage of people who drink either tea or coffee but not both, we can use the principle of inclusion-exclusion. Let's break it down:

Understanding the Percentages

We know that:

• 60% of people drink tea.
• 70% of people drink coffee.

Calculating Overlap

To maximize the percentage of people who drink only one beverage, we need to minimize the overlap (those who drink both tea and coffee). The maximum overlap occurs when the total percentage of tea and coffee drinkers exceeds 100%.

Finding the Maximum Overlap

The total percentage of tea and coffee drinkers is:

60% + 70% = 130%

This means that at least 30% of people must be drinking both beverages (130% - 100% = 30%).

Calculating Exclusive Drinkers

Now, we can find the percentage of people who drink only tea or only coffee:

• Only tea drinkers: 60% - 30% = 30%
• Only coffee drinkers: 70% - 30% = 40%

Final Calculation

The total percentage of people drinking either tea or coffee but not both is:

30% (only tea) + 40% (only coffee) = 70%

Conclusion

The maximum possible percentage of people drinking either tea or coffee but not both is 70%. Therefore, the correct answer is:

B) 70%