Question

The cost of preparing the walls of a room $12m$ long at the rate of $₹1.35$ per square meter is $₹340.20$ and the cost of matting the floor at $85$ paise per square metre is $₹91.80$. Find the height of the room

Answer 1

Given the length of the room $=12m$

Step:$1$

Cost of the matting floor $=$ area of floor $\times$ rate per $m^2$

Area of floor $=$$\frac{Costofmattingfloor}{rateper{m}^2}$

$$\begin{gathered} =\frac{91.8}{0.85} \\ =108m^2 \end{gathered}$$

Breadth of floor $=\frac{area}{length}$

$$\begin{gathered} =\frac{108}{12} \\ =9m \end{gathered}$$

Step:$2$

Area of 4 walls $=$ $\frac{Costofpreparingwalls}{rateper{m}^2}$

$$\begin{gathered} =\frac{340.20}{1.35} \\ =252 \end{gathered}$$

Step:$3$

Total area of walls $=2$(length $+$ breadth)$\times$height

$252=2\left(12+9\right)\times$height

Height $=\frac{252}{42}$

$=6m$

Therefore, the height of the room is $6m$