Question

60 employees in an office were asked about their preference for tea and coffee. It was observed that for every 3 people who prefer tea, there are 2 who prefer coffee. For every 6 people who prefer tea, there are 2 who drink both of tea and coffee. The number of people who drink both is the same as those who drink neither. How many people drink both tea and coffee?

• A. 10
• B. 12
• C. 14
• D. 16

Hint:

Express tea, coffee, both and neither counts in terms of a common ratio unit k, then use the fact that the four non-overlapping groups add up to 60.

Answer 1

The Correct Option is B

Another way to solve this is to express every group directly in terms of a common ratio unit and build a total-count table, rather than writing the inclusion-exclusion formula first.

1. The ratio of tea-drinkers to coffee-drinkers is 3:2, so let tea-drinkers = 3k and coffee-drinkers = 2k for some common unit k.
2. The ratio of tea-drinkers to those who drink both is 6:2, which simplifies to 3:1. Since tea-drinkers = 3k, this means both-drinkers = k.
3. We are told the number who drink neither tea nor coffee equals the number who drink both, so neither-drinkers = k as well.
4. Now count everyone in terms of k. People who drink only tea = tea-drinkers - both = 3k - k = 2k. People who drink only coffee = coffee-drinkers - both = 2k - k = k. People who drink both = k. People who drink neither = k.
5. Adding all four non-overlapping groups gives the total: only tea (2k) + only coffee (k) + both (k) + neither (k) = 5k.
6. Since the office has 60 employees, 5k = 60, so k = 12.
7. The number who drink both tea and coffee is k = 12.

So 12 employees drink both tea and coffee, confirming option (2) as the correct answer.