Question

A room is 8m long and 5m broad. Find the cost of covering the floor of the room with 80cm wide carpet at the rate of Rs. 225 per meter.

Answer 1

Hint: To solve this question, we will first use the formula of the area of a rectangle to calculate the area of the floor, i.e. Area of rectangle = Length x Breadth. Now, because the area of the floor = area of carpet used, then by using this, we will calculate the length of the carpet as breadth = width of the carpet which is given. Finally, we will calculate the total cost by multiplying the length of the carpet with the rate.

Complete step by step answer:
The dimension of the room is given as
The length of the room = 8m. Let us assume this as ‘l’.
\[\Rightarrow l=8m\]
The breadth of the room = 5m. Let us assume this as ‘b’.
\[\Rightarrow b=5m\]
Now because the floor of the room is rectangular in shape, the area of the floor of the room = area of the rectangle.

We know that the area of the rectangle is given as length x breadth.
\[\Rightarrow \text{Area of the floor of room}=l\times b\]
\[\Rightarrow \text{Area of the floor of room}=8\times 5\]
\[\Rightarrow \text{Area of the floor of room}=40{{m}^{2}}\]
Now, because the carpet is going to cover the whole floor of the room, we can write,
Area of carpet = Area of the floor of the room
\[\Rightarrow \text{Area of the carpet}=40{{m}^{2}}........\left( i \right)\]
Now, let the length of the carpet be ‘l’. As, the carpet is again a rectangle, so we can write,
\[\text{Area of the carpet}={{l}^{'}}\times \text{ breadth of the carpet}.........\left( i \right)\]
Width of the carpet = Breadth of the carpet = 80cm
\[\Rightarrow \text{Breadth of the carpet}=80cm=0.8m\]
As by using the unitary method, we have,
\[1m=100cm\]
\[\Rightarrow 100cm=1m\]
\[\Rightarrow 1cm=\dfrac{1}{100}m\]
\[\Rightarrow 80cm=0.8m\]
By using this in equation (ii), we have,
\[\Rightarrow \text{Area of carpet}={{l}^{'}}\times 0.8\]
From equation (i), we have,
\[\Rightarrow 40{{m}^{2}}={{l}^{'}}\times 0.8\]
\[\Rightarrow {{l}^{'}}=\dfrac{40}{0.8}=50m\]
Hence, the length of the carpet is 50m.
Now, the cost of covering the floor of the room can be obtained by multiplying the length of the carpet used to the rate of the carpet.
\[\Rightarrow \text{Cost}=50\times Rs.225\]
\[\Rightarrow \text{Cost}=Rs.11250\]

Therefore, the cost of covering the floor of the room with 80cm wide carpet at the rate Rs. 225 per meter is Rs. 11250.

Note: Students need to observe here that the width of the carpet is given in cm, so always change all the given quantities into a single unit before solving. This can be a possibility of a mistake. One key point to note here is that the cost of the carpet used cannot be calculated directly by multiplying the width with the rate. We need length in place of width to calculate the total cost of covering. So, we have to calculate the length of the carpet by using the area.