Find the cost of carpeting a room 13 m by 9 m with a carpet of width 75 cm at the rate of Rs.105 per metre.

Answer

To find the cost of carpeting a room that measures 13 m by 9 m with a carpet of width 75 cm at the rate of Rs. 105 per meter, we can follow these steps:

### Step 1: Convert the width of the carpet from centimeters to meters.
- Given width of the carpet = 75 cm
- To convert centimeters to meters, we use the conversion factor: 1 cm = 1/100 m.

\[ \text{Width in meters} = \frac{75}{100} = 0.75 \text{ m} \]

### Step 2: Calculate the area of the room.
- The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
- Here, the length of the room = 13 m and the breadth of the room = 9 m.

\[ \text{Area of the room} = 13 \times 9 = 117 \text{ m}^2 \]

### Step 3: Calculate the length of the carpet needed.
- The area covered by the carpet can be calculated using the width of the carpet.
- The area of the carpet can be expressed as:
\[ \text{Area of the carpet} = \text{Length of the carpet} \times \text{Width of the carpet} \]
- Let \( L \) be the length of the carpet. We can set up the equation:

\[ 117 = L \times 0.75 \]

- Solving for \( L \):

\[ L = \frac{117}{0.75} = 156 \text{ m} \]

### Step 4: Calculate the total cost of the carpet.
- The cost of carpeting is given as Rs. 105 per meter.

\[ \text{Total Cost} = \text{Length of the carpet} \times \text{Cost per meter} \]

\[ \text{Total Cost} = 156 \times 105 = 16380 \text{ Rs} \]

### Final Answer:
The total cost of carpeting the room is **Rs. 16,380**.

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