Find the cost of carpeting a room 8 m long and 6 m broad with a carpet 75 cm wide at ? 20 per m.

Options

A. `X 1300`
B. `X 1500`
C. `? 1750`
D. `? 1280`

Answer

To solve the problem of finding the cost of carpeting a room that is 8 m long and 6 m broad with a carpet that is 75 cm wide at a rate of ₹20 per meter, we can follow these steps:

### Step 1: Calculate the area of the room
The area of the room can be calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Given:
- Length = 8 m
- Breadth = 6 m

Calculating the area:
\[ \text{Area} = 8 \, \text{m} \times 6 \, \text{m} = 48 \, \text{m}^2 \]

### Step 2: Convert the width of the carpet from centimeters to meters
The width of the carpet is given as 75 cm. We need to convert this to meters:
\[ \text{Width} = \frac{75 \, \text{cm}}{100} = 0.75 \, \text{m} \]

### Step 3: Calculate the length of the carpet needed
Since the area of the room is equal to the area of the carpet, we can express the area of the carpet as:
\[ \text{Area of Carpet} = \text{Length of Carpet} \times \text{Width of Carpet} \]
Let \( L \) be the length of the carpet needed. We set up the equation:
\[ 48 \, \text{m}^2 = L \times 0.75 \, \text{m} \]

To find \( L \), we rearrange the equation:
\[ L = \frac{48 \, \text{m}^2}{0.75 \, \text{m}} \]

Calculating \( L \):
\[ L = 48 \div 0.75 = 64 \, \text{m} \]

### Step 4: Calculate the cost of the carpet
The cost of carpeting is calculated by multiplying the length of the carpet by the cost per meter:
\[ \text{Cost} = \text{Length of Carpet} \times \text{Cost per meter} \]
Given that the cost per meter is ₹20:
\[ \text{Cost} = 64 \, \text{m} \times 20 \, \text{₹/m} = 1280 \, \text{₹} \]

### Final Answer
The cost of carpeting the room is ₹1280.

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