The cost of carpeting a room 15 m long with a carpet of width 75 cm at Rs.80 per metre is Rs.19200. Find the width of the room.

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the dimensions and costs given in the problem.
- The length of the room is 15 m.
- The width of the carpet is 75 cm, which we need to convert to meters:
\[ 75 \text{ cm} = \frac{75}{100} \text{ m} = 0.75 \text{ m} \]
- The cost of carpeting is Rs. 80 per meter.
- The total cost of carpeting is Rs. 19200.

### Step 2: Calculate the total length of the carpet used.
To find the total length of the carpet used, we can use the formula:
\[ \text{Total Cost} = \text{Cost per meter} \times \text{Total length of carpet} \]
Rearranging this gives us:
\[ \text{Total length of carpet} = \frac{\text{Total Cost}}{\text{Cost per meter}} = \frac{19200}{80} = 240 \text{ m} \]

### Step 3: Calculate the area that the carpet covers.
The area covered by the carpet can be calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]
Here, the width of the carpet is 0.75 m, and the total length of the carpet is 240 m. Therefore:
\[ \text{Area} = 240 \text{ m} \times 0.75 \text{ m} = 180 \text{ m}^2 \]

### Step 4: Relate the area of the room to the dimensions.
Let the width of the room be \( w \) meters. The area of the room can also be expressed as:
\[ \text{Area of the room} = \text{Length} \times \text{Width} = 15 \text{ m} \times w \text{ m} \]
Setting the two area equations equal gives:
\[ 15w = 180 \]

### Step 5: Solve for the width of the room.
To find \( w \), divide both sides by 15:
\[ w = \frac{180}{15} = 12 \text{ m} \]

### Conclusion:
The width of the room is **12 meters**.

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