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

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=(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* b* h\\270=3b* b* h\\90=hb^2\quad \ldots(ii)`

Divide (i) and (ii)

`\Rightarrow (90)/(30)=(b^2h)/(bh)\\\\\Rightarrow b=3\ m`

So, the length of the room is

`l=3b\\l=3* 3\\l=9\ m`

The area of the floor is

`\Rightarrow A_o=l* b\\\Rightarrow A_o=9* 3\\\Rightarrow A_o=27\ m^2`

The cost of flooring is

`\Rightarrow 27* 98\\\Rightarrow Rs.2646`