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

1. 27
2. 28
3. 26
4. 25

Let the average age of people aged 51 years and above be x years.

Let the average age of people aged below 51 years be y years.

Let the number of people aged below 51 years be N.

Given, the average age of all the people in the apartment complex is 38 years.

Therefore,

$\frac{x\times 30+y\times N}{30+N}=38$ ….(1)

We want to maximize y, which occurs when x is minimum i.e. for x=51.

Substituting the value of x in (1) we get

390=N×(38-y)

Again, when y is maximum, N is also maximum i.e. 39

Therefore maximum value of y = 28.

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