Question

The length and breadth of a room are in a ratio 3 : 2. The cost of carpeting the room at Rs 25 per m² is Rs 1350 and the cost of papering the four walls at Rs 15 per m² is Rs 2580. If one door and two windows occupy 8 m², find the dimensions of the room.

Answer 1

Let the length, breadth and height be 3x m, 2x m and h m

Now, area of the floor = $\frac{\mathrm{cost}\mathrm{of}\mathrm{carpeting}}{\mathrm{cost}\mathrm{per}\mathrm{sq}.\mathrm{meter}}=\frac{1350}{25}=54{\mathrm{m}}^2$

$$\begin{gathered} \mathrm{i}.\mathrm{e}.,2x\times 3x=54 \\ \Rightarrow x^2=\frac{54}{6}=9 \\ \Rightarrow x=3 \\ \therefore \mathrm{Length},l=6\mathrm{m}\mathrm{and}\mathrm{breadth},b=9\mathrm{m} \\ \mathrm{Cost}\mathrm{of}\mathrm{papering}\mathrm{the}\mathrm{four}\mathrm{walls}\mathrm{at}\mathrm{Rs}.15\mathrm{per}{\mathrm{m}}^2=\mathrm{Rs}2580 \\ \mathrm{Area}\mathrm{occupied}\mathrm{by}\mathrm{one}\mathrm{door}\mathrm{and}\mathrm{two}\mathrm{windows}=8{\mathrm{m}}^2 \\ \mathrm{Now},\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{walls}=\left(\frac{2580}{15}+8\right){\mathrm{m}}^2=\left(172+8\right){\mathrm{m}}^2=180{\mathrm{m}}^2 \\ \therefore 2\left(l+b\right)\times h=180 \\ \Rightarrow h=\frac{180}{2\left(15\right)}=\frac{180}{30}=6\mathrm{m} \end{gathered}$$