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Explanation:

Maximum people who can like all three drinks is 52 since least number of people linking a particular drink is 52 for lemonade.

Let the number of students liking 
exactly one drink = a
exactly two drinks = b
exactly three drinks = c
exactly no drink = n

⇒ a + 2b + 3c = 73 + 80 + 52 = 205

Even if a = c = 0 and b = 100, a + 2b + 3c = 200
∴ c cannot be zero.

If we shift one student from b to c, the sum will increase by 1.
Hence, to increase the sum by 5, we need to shift 5 students from b to c.

∴ Least possible value of c is 5.

⇒ The difference between the maximum and minimum possible number of students who like all the three drinks = 52 – 5 = 47

Hence, option (b).

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