Question

The cost of a room in a hotel is partially fixed and partially varying with reapect to the number of hours. A person staying for 10 hours paid ₹600 and a person staying for 15 hours paid ₹840. Find the fixed cost and the variable cost per hour.

Answer 1

Let the fixed cost be x and the variable cost per hour be y.
Then,
$x+10y=600$ …(1)
$x+15y=840$ …(2)
Subtracting equation (1) from equation (2), we have,
$5y=240$
$\Rightarrow y=48$
Putting $y=48$ in equation (1), we get $x+10\times 48=600$
$\Rightarrow x=600-480$
$\Rightarrow x=120$
$\therefore$ The fixed cost is ₹120 and the variable cost is ₹48/hr.