Question

The cost of painting the four walls of a room 12 m long at ₹30 per m² is ₹7560 and the cost of covering the floor with mat at ₹25 per m² is ₹2700. Find the dimensions of the room.

Answer 1

$$\begin{gathered} \mathrm{As},\mathrm{the}\mathrm{rate}\mathrm{of}\mathrm{covering}\mathrm{the}\mathrm{floor}=₹25\mathrm{per}{\mathrm{m}}^2 \\ \mathrm{And},\mathrm{the}\mathrm{cost}\mathrm{of}\mathrm{covering}\mathrm{the}\mathrm{floor}=₹2700 \\ \mathrm{So},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{floor}=\frac{2700}{25} \\ \Rightarrow \mathrm{length}\times \mathrm{breadth}=108 \\ \Rightarrow 12\times \mathrm{breadth}=108 \\ \Rightarrow \mathrm{breadth}=\frac{108}{12} \\ \therefore \mathrm{breadth}=9\mathrm{m} \\ \mathrm{Also}, \\ \mathrm{As},\mathrm{the}\mathrm{rate}\mathrm{of}\mathrm{painting}\mathrm{the}\mathrm{four}\mathrm{walls}=₹30\mathrm{per}{\mathrm{m}}^2 \\ \mathrm{And},\mathrm{the}\mathrm{cost}\mathrm{of}\mathrm{painting}\mathrm{the}\mathrm{four}\mathrm{walls}=₹7560 \\ \mathrm{So},\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{four}\mathrm{walls}=\frac{7560}{30} \\ \Rightarrow 2\left(\mathrm{length}+\mathrm{breadth}\right)\mathrm{height}=252 \\ \Rightarrow 2\left(12+9\right)\mathrm{height}=252 \\ \Rightarrow 2\left(21\right)\mathrm{height}=252 \\ \Rightarrow 42\times \mathrm{height}=252 \\ \Rightarrow \mathrm{height}=\frac{252}{42} \\ \therefore \mathrm{height}=6\mathrm{m} \end{gathered}$$

So, the dimensions of the room are $12\mathrm{m}\times 9\mathrm{m}\times 6\mathrm{m}$.