Question

A room is one and a half times long as it is broad. The cost of carpeting the room at $Rs.3.25$ per $m^2$ is $Rs.175.50$ and the cost of papering the walls at $Rs.1.40$ per $m^2$ is $Rs.240.80$. If one door and two windows occupy $8m^2$, find the dimensions of the room.

• A. $15m$
• B. $21m$
• C. $12m$
• D. $6m$

Answer 1

The correct option is A $15m$

Let the breadth of the room be $x$ m.

Therefore, length of the room be $\frac{3x}{2}m$.

Given, cost of carpeting the room at Rs 3.25 per $m^2$ is $Rs.\mathrm{175.50.}$

Total carpet area of the room $=\frac{Rs175.5}{Rs3.25}=54m^2$

$\Rightarrow lb=54\Rightarrow \frac{3x}{2}\times x=54\Rightarrow x^2=36\Rightarrow x=6m$

So, breadth of the room $=6m$ and length of the room $=9m$

Given, cost of papering the walls at Rs. 1.40 per $m^2$ is Rs. $240.80$.

Total area paper on the walls $=\frac{Rs240.80}{1.40}=172m^2$

Given one door and two windows also occupy $8m^2$ area.

Therefore, area of four walls $=172+8=180m^2$

$\Rightarrow 2(l+b)h=180$

$\Rightarrow 2(9+6)h=180$

$\Rightarrow h=6m$

Hence, the dimensions of the room are $9m\times 6m\times 6m.$