Question

The cost of preparing the walls of a room 12 m long at the rate of Rs 30 per m² is Rs 7560, and the cost of covering the floor with mat at Rs 15 per m² is 1620. Find the height of the room

Answer 1

Area of the floor = $\frac{\mathrm{Total}\mathrm{Cost}}{\mathrm{Rate}}=\frac{1620}{15}=108{\mathrm{m}}^2$

∴ Width of the room = $\frac{\mathrm{Area}}{\mathrm{Length}}=\frac{108}{12}=9\mathrm{m}$

Now, let the height of the room be $h$ m.

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{walls}=2(l\times h)+2(b\times h) \\ \Rightarrow \frac{\mathrm{Total}\mathrm{cost}}{\mathrm{Rate}}=2(12\times h)+2(9\times h) \\ \Rightarrow \frac{7560}{30}=\left(2\times 12\times h\right)+\left(2\times 9\times h\right) \\ \Rightarrow 252=24h+18h \\ Or, \\ h=\frac{252}{42}=6 \end{gathered}$$

Thus, the height of the room is 6 m.