Let the total number of people be represented as 100%. If 20% like neither tea nor coffee, then 80% like at least one of the two beverages. By the inclusion–exclusion principle, the percentage who like at least one is the sum of tea-likers and coffee-likers minus those who like both. Thus, 80 = 70 + 40 − (both). Solving this gives (both) = 70 + 40 − 80 = 30%.
Option A:
Option A, 20%, equals the proportion who like neither, not those who like both, and so confuses the outside region with the intersection.
Option B:
Option B calculates the intersection using inclusion–exclusion and ensures that the total does not exceed 100%. It matches the only value that makes the percentages internally consistent.
Option C:
Option C, 40%, would give 70 + 40 − 40 = 70% liking at least one, which contradicts the information that 20% like neither and thus only 80% like at least one.
Option D:
Option D, 50%, creates an even larger overlap and leads to a sum exceeding the allowed total, making the data inconsistent.
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