CAT 2018 Slot 1 QA Question 20: In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex i

Question

In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex i

Accepted Answer

Let there be n people below 51 years of age. Then $n \leq 39$.
To maximize their average age, minimize the total age of the 30 people aged 51 and above.
The minimum possible total age of those 30 people is
$30 	imes 51 = 1530$
If the average age of the below-51 group is x, then
$nx + 1530 \leq 38(n