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?
Explanation:
Let x is average age of 30 people whose age is 51 years and above. Clearly, x ≥ 51
Let y is average age of 39 people whose age is less than 51 years.
∴ 30x + 39y = 69 × 38 ⇒ 10x + 13y = 874
Now to maximise the value of y, we need to minimise the value of x. The least possible value of y = 51.
∴ 10 × 51 + 13y = 874 ⇒ 13y = 874 - 510 = 364 ⇒ y = 364/13 = 28
Thus, the largest possible average age of the people whose ages are below 51 years is 28 years.
Hence, option (b).
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