Question

A room is thrice as long as the breadth. It contains 270m^3 of air and the cost of painting its four walls at Rs 15 per m^2 is Rs. 3600, find the cost of carpeting the floor at Rs. 98 per m^2.

Answer 1

Answer: ₹2646

Step-by-step explanation:

Given

The volume of the room is $V=270\ m^3$

cost of painting the walls is ₹$3600$ at the rate of $15\ m^2$

So, the area of walls is

$\Rightarrow A=\dfrac{3600}{15}\\\\\Rightarrow A=240\ m^2$

This the area of 4 walls i.e.

$\Rightarrow 240=2[hl+hb]\\\Rightarrow 120=h[l+b]\\\Rightarrow 120=4bh\quad [\text{length is thrice of width}]\\\Rightarrow 30=bh\qua \ldots(i)$

The volume of the room is given by

$V=l\times b\times h\\270=3b\times b\times h\\90=hb^2\quad \ldots(ii)$

Divide (i) and (ii)

$\Rightarrow \dfrac{90}{30}=\dfrac{b^2h}{bh}\\\\\Rightarrow b=3\ m$

So, the length of the room is

$l=3b\\l=3\times 3\\l=9\ m$

The area of the floor is

$\Rightarrow A_o=l\times b\\\Rightarrow A_o=9\times 3\\\Rightarrow A_o=27\ m^2$

The cost of flooring is

$\Rightarrow 27\times 98\\\Rightarrow Rs.2646$