A room is 16 m long ,7 m broad and 8 m high. Find the cost of white washing the four walls of room at Rs. 7.5 per `m^(2)`, white washing is not to be done on the doors and windows , which occupy `65 m^2`.

Answer

To find the cost of whitewashing the four walls of a room, we will follow these steps:

### Step 1: Calculate the area of the four walls of the room.
The formula for the area of the four walls of a room is given by:
\[ \text{Area of four walls} = 2 \times (L + B) \times H \]
where \(L\) is the length, \(B\) is the breadth, and \(H\) is the height of the room.

Given:
- Length \(L = 16 \, m\)
- Breadth \(B = 7 \, m\)
- Height \(H = 8 \, m\)

Substituting the values:
\[ \text{Area of four walls} = 2 \times (16 + 7) \times 8 \]
\[ = 2 \times 23 \times 8 \]
\[ = 2 \times 184 \]
\[ = 368 \, m^2 \]

### Step 2: Subtract the area of doors and windows from the total wall area.
The area occupied by doors and windows is given as \(65 \, m^2\).

So, the area to be whitewashed is:
\[ \text{Area to be whitewashed} = \text{Area of four walls} - \text{Area of doors and windows} \]
\[ = 368 \, m^2 - 65 \, m^2 \]
\[ = 303 \, m^2 \]

### Step 3: Calculate the cost of whitewashing.
The cost of whitewashing is given at Rs. 7.5 per \(m^2\).

Thus, the total cost is:
\[ \text{Total cost} = \text{Area to be whitewashed} \times \text{Cost per } m^2 \]
\[ = 303 \, m^2 \times 7.5 \, \text{Rs/m}^2 \]
\[ = 2272.5 \, \text{Rs} \]

### Final Answer:
The total cost of whitewashing the four walls of the room is Rs. 2272.5.

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