# Quantitative Aptitude – Arithmetic – Averages – In an apartment complex, the number ## Slot -1 – Quantitative Aptitude – Arithmetic – Averages – In an apartment complex, the number

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 is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years?

a) 27
b) 25
c) 26
d) 28

Solution:
Let there are n people whose ages are below 51 years. So
Sum of ages of all people = 38×(30+n)
The average age of the people whose ages are below 51 years will be maximum if average age of people aged 51 years or above will be 51 years.
So Sum of ages of these n people = 38(30+n)-51×30=38n-390
So required average age = (38n-390)/n=38-390/n
This will be maximum when n will be maximum and maximum possible value of n = 39
So maximum possible average age of the people whose ages are below 51 years = 38 –390/39=28

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