Question

The cost of papering the walls of the room $12m$ long at the rate of $Rs.1.35$ per $m^2$ is $Rs.340.20$ and the cost of matting the floor at the rate of $85paisa$ per $m^{2}isRs.91.80$. Find the height of the room.

Answer 1

Let $l,b,h$ $=$ length, breadth, height of room

$\Rightarrow$ Area of walls $=2(l+b)h$

$\Rightarrow$ Cost of papering walls $@$ Rs. $1.35$ per $m^2=1.35\times 2hl+b$

$=340.20$

$\Rightarrow h(l+b)=126$

$\Rightarrow h(12+b)=126$

Area of floor $=lb$

$\Rightarrow$ Cost of matting floor $=$ Rs. $\frac{85}{100}\times lb=91.8$

$\Rightarrow lb=108$

$\Rightarrow 12b=108$

$\Rightarrow b=9$ m

$\Rightarrow h\left(21\right)=126$

$\Rightarrow h=6m$.