Question

The ratio between the sides of a room is $5:3$. The cost of white-washing the ceiling of the room at $50$ P per square metre is Rs.$270$ and the cost of papering the walls at $10$ P per square metre is Rs.$48$. The height of the room is ...........

Answer 1

Area of the ceiling
$=\frac{Totalcost}{Costof1sq.unit}$
$=\frac{Rs.270}{0.50.}=540$
$l:b=5:3$ or $l=5x$ and $b=3x$
so that, $5x\times 3x=540m^2$
$\Rightarrow x^2=36m^2$
or $x=6m$
$\therefore$ $l=30m$; $b=18m$
Area of the four walls
$=\frac{Totalcost}{Costof1sq.unit}$
$\therefore Height=\frac{Areaoffourwalls}{2(l+b)}$
$=\frac{480}{2(30+18)}$
$=5m$