A passage 12 m long, 3m high and 4 m wide has two doors of 2.5 m by 1.5 m and a window of 2 m by 0.60 m. The cost of colouring the walls and ceiling at 15 per sq. m is

Options

A. 1023
B. 432
C. 2029.5
D. 1635

Answer

To find the cost of coloring the walls and ceiling of the passage, we will follow these steps:

### Step 1: Calculate the area of the four walls
The formula for the area of the four walls is:
\[ \text{Area of 4 walls} = 2 \times \text{height} \times (\text{length} + \text{breadth}) \]

Given:
- Length = 12 m
- Breadth = 4 m
- Height = 3 m

Substituting the values:
\[ \text{Area of 4 walls} = 2 \times 3 \times (12 + 4) \]
\[ = 2 \times 3 \times 16 \]
\[ = 6 \times 16 = 96 \, \text{m}^2 \]

### Step 2: Calculate the area of the ceiling
The area of the ceiling is given by:
\[ \text{Area of ceiling} = \text{length} \times \text{breadth} \]

Substituting the values:
\[ \text{Area of ceiling} = 12 \times 4 = 48 \, \text{m}^2 \]

### Step 3: Calculate the area of the doors
The area of one door is:
\[ \text{Area of one door} = \text{length} \times \text{breadth} \]

Given:
- Length of door = 2.5 m
- Breadth of door = 1.5 m

Calculating the area of one door:
\[ \text{Area of one door} = 2.5 \times 1.5 = 3.75 \, \text{m}^2 \]

Since there are two doors:
\[ \text{Area of 2 doors} = 2 \times 3.75 = 7.5 \, \text{m}^2 \]

### Step 4: Calculate the area of the window
The area of the window is:
\[ \text{Area of window} = \text{length} \times \text{breadth} \]

Given:
- Length of window = 2 m
- Breadth of window = 0.6 m

Calculating the area of the window:
\[ \text{Area of window} = 2 \times 0.6 = 1.2 \, \text{m}^2 \]

### Step 5: Calculate the total area to be painted
The total area to be painted is given by:
\[ \text{Total area to be painted} = \text{Area of 4 walls} + \text{Area of ceiling} - \text{Area of 2 doors} - \text{Area of window} \]

Substituting the values:
\[ \text{Total area to be painted} = 96 + 48 - 7.5 - 1.2 \]
\[ = 144 - 8.7 = 135.3 \, \text{m}^2 \]

### Step 6: Calculate the cost of coloring
The cost of coloring is given by:
\[ \text{Cost} = \text{Total area to be painted} \times \text{Cost per sq. m} \]

Given:
- Cost per sq. m = Rs. 15

Calculating the total cost:
\[ \text{Cost} = 135.3 \times 15 = 2029.5 \, \text{Rs} \]

### Final Answer
The total cost of coloring the walls and ceiling is Rs. 2029.5.

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