In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is
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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