Question

The central hall of a school is 80 m long and 8 m high. It has 10 doors each of size 3 m $\times$ 1.5 m and 10 windows each of size 1.5 m $\times$ 1 m. If the cost of the white-washing the walls of the hall at the rate of Rs. 1.20 per $m^2$ is Rs. 2385.60, find the breadth of the hall.

Answer 1

Lenght of hall (l) = 80 m
Height (h)= 8 m
Size of each door = 3 m $\times$ 1.5 m
$\therefore$ Area of 10 doors = $3\times 1.5\times 10m^2$
= 45 $m^2$
A size of each windows = 1.5 m $\times$ 1 m
$\therefore$ Area of 10 windows
= $1.5m\times 1\times 10=15m^2$
Total cost of whitewashing the walls = Rs. 2385.60
Rate of whitewashing =Rs. 1.20 per $m^2$
$\therefore$ Area of walls which are whitewashed
= $\frac{2385.60}{1.20}=1988m^2$
$\therefore$ Total area of four walls including doors and windows = 1988+45+15 = 2048
$2(l+b)\times h=2048=2(l+b)\times 8=2048$
$l+b=\frac{2048}{2\times 8}=128m$
$\Rightarrow$ 80+b = 128 $\Rightarrow$ b= 128-80= 48
$\therefore$ Breadth of hall = 48 m