Question

the cost of painting 4walls of room 4m high is rs15 per meter square is rs2400.if breadth of room is two third of its length what will be the cost of carpeting the floor at rs 200 per meter square?​

Answer 1

The cost of carpeting the room is Rs 19,200

Explanation:

Given as :

The height of the four wall = h = 4 meters

The cost of painting the wall at the rate of rs 15 per square meter = rs 2400

The length of room = L

The breadth of room = b =
`(2)/(3)` of length

i.e b =
`(2 L)/(3)`

Let The cost of carpeting the room =rs x

Now, According to question

∵Area of 4 wall = 2 × (Length + breadth)× height

i.e Area = 2 × (L + b)× h

Or, Area = 2 × (L +
`(2 L)/(3)` )× 4

Or, Area =
`(40 L)/(3)`

Now,

The cost of painting the wall at the rate of rs 15 per square meter = rs 2400

∴ The cost of painting the 4 wall =
`(2400)/(15)`

i.e
`(40 L)/(3)` = 160

Or, L =
`(160* 3)/(40)`

So, length = L = 12 meters

The breadth = b =
`(2 L)/(3)`

i.e breadth =
`(2* 12)/(3)`

Or, breadth = 8 meters

Again

Area of rectangular room = length × breadh

i.e Area of rectangular room = 12 meters × 8 meters

Or, Area of rectangular room = 96 meters²

Now,

The cost of carpeting the room at rs 200 per meters² = area of room × rate of carpeting

i.e x = 96 meters² × 200 per meters²

Or, x = rs 19,200

So, The cost of carpeting the room = x = rs 19,200

Hence, The cost of carpeting the room is Rs 19,200 Answer