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

Step 1: Set up the ratios using a common unit k.
Let the number of people who prefer tea be T, coffee be C, both be X, and neither be N.
Tea to coffee ratio is 3:2, so T = 3k and C = 2k for some unit k.
Step 2: Use the tea-to-both ratio.
Tea to both ratio is 6:2, which simplifies to 3:1. Since T = 3k, this means X = k.
Step 3: Use the condition that both equals neither.
N = X = k.
Step 4: Apply the inclusion-exclusion principle for the total.
Total employees = (people who drink tea or coffee) + (people who drink neither) = (T + C - X) + N.
This is because T + C counts the "both" group twice, so X is subtracted once to correct for the overlap, and then N is added for people outside both groups.
Step 5: Substitute the values in terms of k.
(3k + 2k - k) + k = 60, which simplifies to 4k + k = 60, so 5k = 60.
Step 6: Solve for k.
k = 12.
Step 7: Find the number who drink both.
Both = X = k = 12, which matches option (2).