The cost of carpeting a room 15 m long with a carpet 75 cm wide , at Rs. 70 per metre , is Rs. 8400 .The width of the room is

Options

A. 9m
B. 8m
C. 6m
D. 12m

Explanation

To find the width of the room, we can follow these steps:

### Step 1: Convert the width of the carpet from centimeters to meters.
The width of the carpet is given as 75 cm. To convert this to meters, we divide by 100.

\[ \text{Width of the carpet in meters} = \frac{75 \text{ cm}}{100} = 0.75 \text{ m} \]

### Step 2: Calculate the total length of the carpet used.
The total cost of carpeting is Rs. 8400, and the cost per meter is Rs. 70. To find the total length of the carpet used, we divide the total cost by the cost per meter.

\[ \text{Total length of carpet} = \frac{8400 \text{ Rs}}{70 \text{ Rs/m}} = 120 \text{ m} \]

### Step 3: Calculate the area covered by the carpet.
The area covered by the carpet can be calculated using the formula for area (Area = Length × Width).

\[ \text{Area covered by carpet} = \text{Total length of carpet} \times \text{Width of carpet} \]
\[ \text{Area covered by carpet} = 120 \text{ m} \times 0.75 \text{ m} = 90 \text{ m}^2 \]

### Step 4: Find the width of the room using the area.
The area of the room can also be expressed as the product of its length and width. Given that the length of the room is 15 m, we can let the width of the room be \( w \).

\[ \text{Area of the room} = \text{Length} \times \text{Width} = 15 \text{ m} \times w \]

Since the area covered by the carpet is equal to the area of the room, we can set the two equations equal to each other:

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

### Step 5: Solve for the width of the room.
To find \( w \), we can rearrange the equation:

\[ w = \frac{90 \text{ m}^2}{15 \text{ m}} = 6 \text{ m} \]

Thus, the width of the room is **6 meters**.

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