Find the cost of covering the floor of a rectangular corridor 90 m by 2.7 m with carpet 90 cm wide at rupes 76 per meter.

Answer

To find the cost of covering the floor of a rectangular corridor with carpet, we can follow these steps:

### Step 1: Find the Area of the Corridor
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]

Given:
- Length of the corridor = 90 m
- Width of the corridor = 2.7 m

Calculating the area:
\[ \text{Area} = 90 \, \text{m} \times 2.7 \, \text{m} = 243 \, \text{m}^2 \]

### Step 2: Convert the Width of the Carpet to Meters
The width of the carpet is given in centimeters. We need to convert it to meters:
\[ \text{Width of carpet} = 90 \, \text{cm} = \frac{90}{100} \, \text{m} = 0.9 \, \text{m} \]

### Step 3: Calculate the Length of the Carpet Required
The area of the carpet must equal the area of the corridor. The area of the carpet can be calculated as:
\[ \text{Area of carpet} = \text{Length} \times \text{Width} \]
Let the length of the carpet be \( l \):
\[ l \times 0.9 \, \text{m} = 243 \, \text{m}^2 \]

Now, solving for \( l \):
\[ l = \frac{243 \, \text{m}^2}{0.9 \, \text{m}} = 270 \, \text{m} \]

### Step 4: Calculate the Cost of the Carpet
The cost of the carpet is given as 76 rupees per meter. Therefore, the total cost can be calculated as:
\[ \text{Total Cost} = \text{Length of carpet} \times \text{Cost per meter} \]
\[ \text{Total Cost} = 270 \, \text{m} \times 76 \, \text{rupees/m} \]

Calculating the total cost:
\[ \text{Total Cost} = 270 \times 76 = 20520 \, \text{rupees} \]

### Final Answer
The cost of covering the floor of the corridor with carpet is **20520 rupees**.

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