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

Answer 1

The Correct Option is B

To solve this problem, let's use a systematic approach using algebra. Let \( T \) be the number of people who prefer tea, \( C \) be the number of people who prefer coffee, and \( B \) be the number of people who drink both tea and coffee. Also, let \( N \) be those who drink neither.

1. According to the problem, for every 3 who prefer tea, 2 prefer coffee. This gives us the ratio:

\[\frac{T}{C} = \frac{3}{2}\]

Therefore, \( T = \frac{3}{2}C \) or \( C = \frac{2}{3}T \).

2. It also states that for every 6 people who prefer tea, 2 drink both tea and coffee. Therefore:

\[\frac{T}{B} = \frac{6}{2} = 3\]

This implies \( T = 3B \).

3. The number of people who drink both is the same as those who drink neither, so \( B = N \).

4. The total number of people is the sum of people who prefer only tea, only coffee, both, and neither:

\[T + C - B + N = 60\]

Substituting \( B = N \) into the equation:

\[T + C = 60\]

5. Substitute the expressions from steps 1 and 2 into this equation:

\[3B + \frac{2}{3}(3B) = 60\]
\[3B + 2B = 60\]
\[5B = 60\]
\[B = 12\]

We conclude that \( \boxed{12} \) people drink both tea and coffee.