Question

Find the cost of Carpeting a room 12 m Long and 8 m broad with a carpet 75 cm broad at the rate of \[{\text{Rs}}116.50\] per meter.

Answer 1

Hint: Here we need to find the cost of carpeting the room of given length and thickness. We will first find the area of the room using the given dimensions and then we will use this area to find the length of the carpet. Then we will find the cost of carpeting the room.

Complete step-by-step answer:
Here we need to find the cost of carpeting the room of given length and thickness.
Length of the room $ = 12m$
Breadth of the room $ = 8m$
We will first find the area of the floor of the room. The room is rectangular in shape. We know that the area rectangle is equal to the product of the breadth and length of the rectangle.
Therefore,
Area of room $ = 12m \times 8m$
On multiplying the numbers, we get
Area of room $ = 96{m^2}$.
The given width of the carpet $ = 75cm$
We will first convert the unit of the breadth in centimeter.
We know that $1cm = \dfrac{1}{{100}}m$
Therefore,
Width of the carpet $ = 75 \times \dfrac{1}{{100}}m$
On multiplying terms, we get
Width of the carpet $ = 0.75m$
As the area of carpet required will be same as the area of the room.
Area of the carpet required $ = 96{m^2}$ ………….. $\left( 1 \right)$
Now, we will find the length of the carpet. We can write equation 1 as
$ \Rightarrow {\text{length}} \times {\text{breadth}} = 96{m^2}$
Now, we will substitute the value of breadth of the carpet.
$ \Rightarrow {\text{length}} \times 0.75m = 96{m^2}$
Now, we will divide both sides by 0.75 m.
$ \Rightarrow \dfrac{{{\text{length}} \times 0.75m}}{{0.75m}} = \dfrac{{96{m^2}}}{{0.75m}}$
On further simplification, we get
$ \Rightarrow {\text{length}} = 128m$
We know that the rate of carpet is \[{\text{Rs}}116.50\] per meter.
Therefore, cost of carpeting $ = {\text{length}} \times {\text{rate of carpet}}$
Now, we will substitute the value of length and rate of the carpet here.
$ \Rightarrow$ Cost of carpeting $ = 128 \times 116.50$
On multiplying the numbers, we get
$ \Rightarrow$ Cost of carpeting $ = Rs14912$
Hence, this is the required answer.

Note: Here we have obtained the cost of carpeting the floor of the room. We need to remember that the area of carpet required for the room will be the same as the area of the floor of the room. Hence, we will use the area of the room to find the length of the carpet. The area is defined as the space occupied by a two-dimensional surface.