The length of a room is 15 m. The cost of carpeting it with a carpet 75 cm wide at Rs.50 per metre is Rs.6000. The width of the room is

Options

A. 6m
B. 8m
C. 13.4m
D. 18m

Answer

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

### Step 1: Understand the given information
- Length of the room = 15 m
- Width of the carpet = 75 cm = 0.75 m (since 1 m = 100 cm)
- Cost of carpeting = Rs. 6000
- Cost per meter of carpet = Rs. 50

### Step 2: Calculate the total length of the carpet used
To find the total length of the carpet used, we can use the formula:

\[ \text{Total Length of Carpet} = \frac{\text{Total Cost}}{\text{Cost per meter}} \]

Substituting the values:

\[ \text{Total Length of Carpet} = \frac{6000}{50} = 120 \text{ m} \]

### Step 3: Calculate the area covered by the carpet
The area covered by the carpet can be calculated using the formula:

\[ \text{Area} = \text{Length} \times \text{Width} \]

Substituting the values:

\[ \text{Area of Carpet} = 120 \text{ m} \times 0.75 \text{ m} = 90 \text{ m}^2 \]

### Step 4: Relate the area of the room to its dimensions
The area of the room can also be expressed as:

\[ \text{Area of Room} = \text{Length} \times \text{Width} \]

We know the length of the room is 15 m, so we can express the width (W) of the room as:

\[ 90 \text{ m}^2 = 15 \text{ m} \times W \]

### Step 5: Solve for the width of the room
To find the width, we rearrange the equation:

\[ W = \frac{90}{15} = 6 \text{ m} \]

### Conclusion
The width of the room is **6 meters**.

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