Question

The cost of carpeting the floor of a room, whose breadth is twice it’s height and length is twice it’s breadth, at the rate of Rs.540 m² is Rs. 64,000. What will be the cost of plastering its 4 walls at the rate of Rs 20 per square meter.

Answer 1

The cost of plastering the four wall at the rate of Rs 20 per meter square is Rs 3,543.4

Explanation:

Given as :

The cost of carpeting a room = Rs 64,000

The rate of carpeting = Rs 540 m²

The breadth is twice its height

The length is twice its breadth

Let The length = L m

The breadth = B m

The height = L m

So, according to question

L = 2 B and B = 2 H

Now, Area of rectangular carpet = Length × Breadth

Or, A = L × B

Or, A = 2 B × B

∵ The cost of carpeting at the rate of Rs 540 per m² = Rs 64,000

So, area =
`(64000)/(540)`

Or, 2× B² = 118.518

Or, B² =
`(118.518)/(2)`

Or, B² = 59.259

I,.e B =
`√(59.259)` = 7.69 m

The length = 2 B

I.e L = 2 × 7.69 = 15.38 m

and H =
`(B)/(2)`

I.e H =
`(7.69)/(2)` = 3.84 m

So, Length = 15.38 m , Breadth = 7.69 m , height = 3.84 m

∵ The area of four wall = 2× ( Length + Breadth ) × height

or, The area of four wall = 2× ( 15.38 + 7.69 ) × 3.84

Or, The area of four wall = 177.17 m²

Now The rate of plastering the four wall = Rs 20 per square meter

So, The cost of plastering the four wall = area of four wall × rs 20

∴ The cost of plastering the four wall = 177.17 × Rs 20

I.e The cost of plastering the four wall = Rs 3,543.4

Hence The cost of plastering the four wall at the rate of Rs 20 per meter square is Rs 3,543.4 answer