The length, breadth and height of a room are 7.5 m, 4.5 m and 3.0 m respectively. There is a door of measure `2.0 m xx 1.0 m` and also 2 windows each of measure 1.2 m and 0.75 m. Find the cost of white washing its walls and roof at the rate of Rs. 1.20 per square metre.

Answer

To find the cost of whitewashing the walls and roof of the room, we will follow these steps:

### Step 1: Calculate the surface area of the walls and the roof.
The room has four walls and a roof. The formula for the area of the walls is:
\[ \text{Area of walls} = 2 \times \text{height} \times (\text{length} + \text{breadth}) \]
And the area of the roof (ceiling) is:
\[ \text{Area of roof} = \text{length} \times \text{breadth} \]

Given:
- Length (l) = 7.5 m
- Breadth (b) = 4.5 m
- Height (h) = 3.0 m

Calculating the area of the walls:
\[ \text{Area of walls} = 2 \times 3.0 \times (7.5 + 4.5) \]
\[ = 2 \times 3.0 \times 12.0 \]
\[ = 72.0 \, \text{m}^2 \]

Calculating the area of the roof:
\[ \text{Area of roof} = 7.5 \times 4.5 \]
\[ = 33.75 \, \text{m}^2 \]

Total area of walls and roof:
\[ \text{Total area} = \text{Area of walls} + \text{Area of roof} \]
\[ = 72.0 + 33.75 \]
\[ = 105.75 \, \text{m}^2 \]

### Step 2: Calculate the area of the door and windows.
The area of the door:
\[ \text{Area of door} = 2.0 \times 1.0 = 2.0 \, \text{m}^2 \]

The area of one window:
\[ \text{Area of one window} = 1.2 \times 0.75 = 0.9 \, \text{m}^2 \]
Since there are 2 windows:
\[ \text{Area of two windows} = 2 \times 0.9 = 1.8 \, \text{m}^2 \]

### Step 3: Calculate the total area to be whitewashed.
Total area to be subtracted (door + windows):
\[ \text{Total area of openings} = \text{Area of door} + \text{Area of two windows} \]
\[ = 2.0 + 1.8 = 3.8 \, \text{m}^2 \]

Net area to be whitewashed:
\[ \text{Net area} = \text{Total area} - \text{Total area of openings} \]
\[ = 105.75 - 3.8 \]
\[ = 101.95 \, \text{m}^2 \]

### Step 4: Calculate the cost of whitewashing.
The cost of whitewashing per square meter is Rs. 1.20.
Total cost:
\[ \text{Total cost} = \text{Net area} \times \text{Cost per square meter} \]
\[ = 101.95 \times 1.20 \]
\[ = 122.34 \, \text{Rs} \]

### Final Answer:
The cost of whitewashing the walls and roof of the room is Rs. 122.34.

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