Question

The length of a room is $50$ per cent more than its breadth. The cost of carpeting the room at the rate of $Rs38.50m^2$ is $Rs924$ and the cost of painting the walls at the rate of $Rs5.50$ per $m^2$ is $Rs1,320$. Find the dimensions of the room.

Answer 1

Let length $\left(l\right)=\frac{x+1}{2x}=\frac{3}{2\left(x\right)}$

Let breadth $\left(b\right)=x$

Area of floor $=\frac{924\times 100}{3850}$

$l\times b=24$

$\frac{3x}{2}\times x=24\Rightarrow x^2=\frac{24\times 2}{3}$

$\frac{3}{2}{x}^2=24$ $x=4$

Area of walls $=1320\times \frac{100}{550}$

$2(l+b)h=240$

$100\times h=\frac{240}{2}$

$h=12m$

$l=\frac{3}{2}\times 4=6cm$

$b=x=4cm$