The floor of a corridor is 100 m long and 3m wide. Cost of covering the floor with carpet 50 cm wide at the rate of Rs. 15 per m is

Options

A. Rs. 4500
B. Rs. 9000
C. Rs. 7500
D. Rs. 1900

Answer

To solve the problem step by step, we need to calculate the total cost of covering the floor of the corridor with the carpet. Here’s how we can do that:

### Step 1: Calculate the area of the corridor
The area of the corridor can be calculated using the formula for the area of a rectangle:
\[ \text{Area} = \text{Length} \times \text{Width} \]
Given that the length of the corridor is 100 m and the width is 3 m:
\[ \text{Area} = 100 \, \text{m} \times 3 \, \text{m} = 300 \, \text{m}^2 \]

### Step 2: Convert the width of the carpet from centimeters to meters
The width of the carpet is given as 50 cm. To convert this into meters:
\[ 50 \, \text{cm} = \frac{50}{100} \, \text{m} = 0.5 \, \text{m} \]

### Step 3: Calculate the length of the carpet needed
The area of the carpet must equal the area of the corridor. The area of the carpet can also be expressed as:
\[ \text{Area of carpet} = \text{Length of carpet} \times \text{Width of carpet} \]
Let \( L \) be the length of the carpet. Therefore:
\[ 300 \, \text{m}^2 = L \times 0.5 \, \text{m} \]
To find \( L \):
\[ L = \frac{300 \, \text{m}^2}{0.5 \, \text{m}} = 600 \, \text{m} \]

### Step 4: Calculate the total cost of the carpet
The cost of the carpet is given at the rate of Rs. 15 per meter. Therefore, the total cost can be calculated as:
\[ \text{Total Cost} = \text{Length of carpet} \times \text{Rate per meter} \]
Substituting the values:
\[ \text{Total Cost} = 600 \, \text{m} \times 15 \, \text{Rs/m} = 9000 \, \text{Rs} \]

### Final Answer
The total cost of covering the floor with carpet is Rs. 9000.

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