A room is 19 m long and 3.50 m broad. What will be the cost of covering its floor with a carpet of 70 cm wide at 95 paise per metre ?

Options

A. Rs. 90.25
B. Rs. 99.25
C. Rs. 90.75
D. none of these

Answer

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

### Step 1: Calculate the Area of the Room
The area of the room can be calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Given:
- Length = 19 m
- Breadth = 3.50 m

Calculating the area:
\[ \text{Area} = 19 \, \text{m} \times 3.50 \, \text{m} = 66.5 \, \text{m}^2 \]

### Step 2: Convert the Width of the Carpet from cm to m
The width of the carpet is given in centimeters (70 cm). We need to convert this to meters:
\[ \text{Width of carpet} = \frac{70 \, \text{cm}}{100} = 0.7 \, \text{m} \]

### Step 3: Calculate the Length of Carpet Required
To find the length of carpet needed to cover the entire area of the room, we can use the formula:
\[ \text{Area of Carpet} = \text{Length of Carpet} \times \text{Width of Carpet} \]
Setting the area of the carpet equal to the area of the room:
\[ 66.5 \, \text{m}^2 = \text{Length of Carpet} \times 0.7 \, \text{m} \]
Now, solving for the length of the carpet:
\[ \text{Length of Carpet} = \frac{66.5 \, \text{m}^2}{0.7 \, \text{m}} = 95 \, \text{m} \]

### Step 4: Calculate the Cost of the Carpet
The cost of carpeting is given as 95 paise per meter. To find the total cost for 95 meters:
\[ \text{Total Cost} = \text{Length of Carpet} \times \text{Cost per meter} \]
Calculating the total cost:
\[ \text{Total Cost} = 95 \, \text{m} \times 95 \, \text{paisa/m} = 9025 \, \text{paisa} \]

### Step 5: Convert the Cost from Paisa to Rupees
Since 100 paisa = 1 rupee, we convert the total cost into rupees:
\[ \text{Total Cost in Rupees} = \frac{9025 \, \text{paisa}}{100} = 90.25 \, \text{rupees} \]

### Final Answer
The cost of covering the floor with the carpet is **90.25 rupees**.

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