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. 26
2. 27
3. 28
4. 25

Answer 1

Correct Answer - Option 3 : 28

Calculation:

Let number of people aged below 51 years be n.

Total number of people in a complex = 30 + n

Total age of people in a complex = (30 + n) × 38

Largest possible average age of people above 51 years is 51.

Total age of people above 51 years = 51 × 30

Total age of people below 51 years = (30 + n) × 38 - 51 × 30 = 38n - 390

Average age people below 51 years = (38n - 390)/n

Then,

For largest possible age, n = 39

∴ Required age = (38 - 390/39) = 28 years