CAT 2018 Question Paper Shift 1 Solved Paper

Let the average age of people aged 51 years and above be $\mathit{x}$ years.
Let the average age of people aged below 51 years be y years.
Let the number of people aged below 51 years be $\mathit{N}$.
Let the number of people aged below 51 years be $\mathit{N}$.
Given, the average age of all the people in the apartment complex is 38 years.
Therefore,
$\frac{\mathit{x}\times 30+\mathit{y}\times \mathit{N}}{30+\mathit{N}}=38$.....(1)
We want to maximize $\mathit{y}$, which occurs when $\mathit{x}$ is minimum i.e. for $\mathit{x}=51$.
Substituting the value of $\mathit{x}$ in (1) we get
$390=\mathit{N}\times \left(38-\mathit{y}\right)$
Again, when $\mathit{y}$ is maximum, $\mathit{N}$ is also maximum i.e. 39
Therefore maximum value of $\mathit{y}=28$.