The dining hall of a hotel is 75 m . Long 60m broad and 16 m high It has five doors 4m by 3 m each and four windows 3 m by 1.6 m each. Find the cost of:
(i) papering its walls at the rate of rupees 12 per `m ^(2)`
(ii) Carpeting its floor at the rate of rupees ` 25 " per " m^(2)`

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the area of the walls of the dining hall.
The formula for the area of the walls of a rectangular room is given by:

\[ \text{Area of walls} = 2h(l + b) \]

Where:
- \( h \) = height of the hall = 16 m
- \( l \) = length of the hall = 75 m
- \( b \) = breadth of the hall = 60 m

Substituting the values:

\[ \text{Area of walls} = 2 \times 16 \times (75 + 60) \]
\[ = 32 \times 135 \]
\[ = 4320 \, \text{m}^2 \]

### Step 2: Calculate the area of the doors and windows.
**Area of doors:**
There are 5 doors, each measuring \( 4 \, \text{m} \times 3 \, \text{m} \).

\[ \text{Area of doors} = 5 \times (4 \times 3) = 5 \times 12 = 60 \, \text{m}^2 \]

**Area of windows:**
There are 4 windows, each measuring \( 3 \, \text{m} \times 1.6 \, \text{m} \).

\[ \text{Area of windows} = 4 \times (3 \times 1.6) = 4 \times 4.8 = 19.2 \, \text{m}^2 \]

### Step 3: Calculate the total area to be papered.
Now, we subtract the area of the doors and windows from the total area of the walls:

\[ \text{Area to be papered} = \text{Area of walls} - \text{Area of doors} - \text{Area of windows} \]
\[ = 4320 - 60 - 19.2 \]
\[ = 4320 - 79.2 = 4240.8 \, \text{m}^2 \]

### Step 4: Calculate the cost of papering the walls.
The cost of papering is given at the rate of Rs. 12 per m².

\[ \text{Cost of papering} = \text{Area to be papered} \times \text{Rate} \]
\[ = 4240.8 \times 12 \]
\[ = 50889.6 \, \text{Rs} \]

### Step 5: Calculate the area of the floor.
The area of the floor can be calculated using the formula:

\[ \text{Area of floor} = l \times b \]
\[ = 75 \times 60 \]
\[ = 4500 \, \text{m}^2 \]

### Step 6: Calculate the cost of carpeting the floor.
The cost of carpeting is given at the rate of Rs. 25 per m².

\[ \text{Cost of carpeting} = \text{Area of floor} \times \text{Rate} \]
\[ = 4500 \times 25 \]
\[ = 112500 \, \text{Rs} \]

### Final Answers:
(i) Cost of papering the walls: Rs. 50889.6
(ii) Cost of carpeting the floor: Rs. 112500

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