In an apartment complex, the number of people aged 51 years and above

In the following solution, the two groups of occupants are referred to as Groups A (those whose ages are 51 or more years) and B(those whose ages are below 51 years). It is assumed that the average age and the number of occupants in B are 'x' years and 'y' respectively.

SOLUTION

01. Since the average age of all occupants is fixed it stands to reason that the lowest average age be assumed for the occupants of A in order to maximize the average age of the occupants of B. Thus the total age of all occupants in A is 51*30=1530. Total age of occupants in B is, of course, x*y.
02. (Total age of all occupants in the apartment complex)/(Total number of occupants in the complex)=Average age of all occupants
(1530+xy)/(30+y)=38---> xy=38y-390---> x=(38y-390)/y---> x=38-(390/y). In order to maximize the value of 'x' we have to minimize the value of 390/y which means that we have to maximize the value of 'y'. But the maximum value of 'y' is limited to 39. Therefore:
x=38-(390/39)=38-10=28.

Ans: D