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

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the area of the room
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Given:
- Length of the room = 8 m
- Breadth of the room = 5 m

Substituting the values:
\[ \text{Area} = 8 \, \text{m} \times 5 \, \text{m} = 40 \, \text{m}^2 \]

### Step 2: Determine the width of the carpet in meters
The width of the carpet is given as 80 cm. We need to convert this measurement into meters:
\[ 80 \, \text{cm} = \frac{80}{100} \, \text{m} = 0.8 \, \text{m} \]

### Step 3: Calculate the length of the carpet needed
Let \( l_1 \) be the length of the carpet. The area of the carpet must equal the area of the room, so we set up the equation:
\[ l_1 \times \text{Width of carpet} = \text{Area of room} \]
Substituting the known values:
\[ l_1 \times 0.8 \, \text{m} = 40 \, \text{m}^2 \]
To find \( l_1 \):
\[ l_1 = \frac{40 \, \text{m}^2}{0.8 \, \text{m}} = 50 \, \text{m} \]

### Step 4: Calculate the cost of the carpet
The cost of the carpet is calculated by multiplying the length of the carpet by the rate per meter:
\[ \text{Cost} = \text{Length of carpet} \times \text{Rate per meter} \]
Given:
- Rate = Rs 225 per meter

Now substituting the values:
\[ \text{Cost} = 50 \, \text{m} \times 225 \, \text{Rs/m} = 11250 \, \text{Rs} \]

### Final Answer
The total cost of covering the floor of the room with the carpet is Rs 11,250.

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