A room 8 m long, 6 m broad and 3 m high has two windows of `(3)/(2)mxx1m` and a door of `2mxx(1)/(2)m` Find the cost of papering the walls with paper 50 cm wide at 25 paise per meter.

Options

A. Rs. 30
B. Rs. 40
C. Rs. 50
D. Rs. 70

Answer

To find the cost of papering the walls of the room, we need to follow these steps:

### Step 1: Calculate the Area of the Walls
The room has four walls. The dimensions of the walls are as follows:
- Two walls of dimensions \(8 \, \text{m} \times 3 \, \text{m}\)
- Two walls of dimensions \(6 \, \text{m} \times 3 \, \text{m}\)

**Area of the two longer walls:**
\[ \text{Area} = 2 \times (8 \, \text{m} \times 3 \, \text{m}) = 2 \times 24 \, \text{m}^2 = 48 \, \text{m}^2 \]

**Area of the two shorter walls:**
\[ \text{Area} = 2 \times (6 \, \text{m} \times 3 \, \text{m}) = 2 \times 18 \, \text{m}^2 = 36 \, \text{m}^2 \]

**Total area of the walls:**
\[ \text{Total Area} = 48 \, \text{m}^2 + 36 \, \text{m}^2 = 84 \, \text{m}^2 \]

### Step 2: Calculate the Area of the Windows and Door
**Area of the two windows:**
Each window has dimensions of \(\frac{3}{2} \, \text{m} \times 1 \, \text{m}\).
\[ \text{Area of one window} = \frac{3}{2} \, \text{m} \times 1 \, \text{m} = \frac{3}{2} \, \text{m}^2 \]
\[ \text{Area of two windows} = 2 \times \frac{3}{2} \, \text{m}^2 = 3 \, \text{m}^2 \]

**Area of the door:**
The door has dimensions of \(2 \, \text{m} \times \frac{1}{2} \, \text{m}\).
\[ \text{Area of the door} = 2 \, \text{m} \times \frac{1}{2} \, \text{m} = 1 \, \text{m}^2 \]

### Step 3: Calculate the Total Area to be Papered
Now, we subtract the area of the windows and the door from the total area of the walls:
\[ \text{Area to be papered} = \text{Total Area of Walls} - \text{Area of Windows} - \text{Area of Door} \]
\[ \text{Area to be papered} = 84 \, \text{m}^2 - 3 \, \text{m}^2 - 1 \, \text{m}^2 = 80 \, \text{m}^2 \]

### Step 4: Calculate the Length of Wallpaper Required
The width of the wallpaper is \(50 \, \text{cm} = 0.5 \, \text{m}\). To find the length of wallpaper required, we divide the area to be papered by the width of the wallpaper:
\[ \text{Length of wallpaper required} = \frac{\text{Area to be papered}}{\text{Width of wallpaper}} = \frac{80 \, \text{m}^2}{0.5 \, \text{m}} = 160 \, \text{m} \]

### Step 5: Calculate the Cost of Papering
The cost of papering is given as \(25 \, \text{paise per meter}\). Therefore, the total cost will be:
\[ \text{Total Cost} = \text{Length of wallpaper required} \times \text{Cost per meter} = 160 \, \text{m} \times 0.25 \, \text{rupees} = 40 \, \text{rupees} \]

### Final Answer
The cost of papering the walls is **40 rupees**.

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