CAT Exam 2021 Slot 3 Solved Paper

$\Profit \per \boarder = {\Total \profit} / {\Number \of \boarders}$
Let the number of boarders be $n$
$\Profit/\boarder = 1600 - {\Total \cost}/n $
Let the total cost be $a + bn$, where $a = \fixed$, and $b$ is the variable
additional cost per boarder.
$ \Profit/\boarder = 1600 - (\a + \bn)/\n$
$ \Profit/\boarder = 1600 - \a/\n - \b $
$1600 - \a/50 - \b = 200$
$ 1600 - \a/75 - \b = 250 $
Solving, we get $ a = 7500$ and $b = 1250 $
Hence, total profit with $80 \people$ $= 80 ( 1600 - 7500/80 - 1250) = 80 (350 - 7500/80) = 28000 - 7500$ = Rs. 20500