A room is 36 m long, 12 m wide and 10 m high . It has 6 window , each ` 3m xx 2.5 m `, one door ` 9.5m xx 6 m and ` one fire chimney ` 4m xx 4.5`. Find the expenditure of papering its walls at the rate of 70 paise per metre , if the width of the paper is 1.2 m :

Options

A. a. Rs. 490
B. b. Rs. 690
C. c. Rs. 1000
D. d. none of these

Answer

To solve the problem step by step, we will follow the given information and apply the relevant formulas.

### Step 1: Calculate the Area of the Four Walls
The formula for the area of the four walls of a room is:
\[ \text{Area} = 2 \times \text{Height} \times (\text{Length} + \text{Width}) \]
Given:
- Length (L) = 36 m
- Width (B) = 12 m
- Height (H) = 10 m

Substituting the values:
\[ \text{Area} = 2 \times 10 \times (36 + 12) = 2 \times 10 \times 48 = 960 \, \text{m}^2 \]

### Step 2: Calculate the Total Area of Openings (Windows, Door, and Chimney)
1. **Area of Windows**:
Each window has dimensions of 3 m x 2.5 m, and there are 6 windows.
\[ \text{Area of windows} = 6 \times (3 \times 2.5) = 6 \times 7.5 = 45 \, \text{m}^2 \]

2. **Area of the Door**:
The door has dimensions of 9.5 m x 6 m.
\[ \text{Area of door} = 9.5 \times 6 = 57 \, \text{m}^2 \]

3. **Area of the Chimney**:
The chimney has dimensions of 4 m x 4.5 m.
\[ \text{Area of chimney} = 4 \times 4.5 = 18 \, \text{m}^2 \]

4. **Total Area of Openings**:
\[ \text{Total area of openings} = \text{Area of windows} + \text{Area of door} + \text{Area of chimney} = 45 + 57 + 18 = 120 \, \text{m}^2 \]

### Step 3: Calculate the Area to be Papered
To find the area that needs to be papered, subtract the total area of openings from the total area of the walls:
\[ \text{Area to be papered} = \text{Area of walls} - \text{Total area of openings} = 960 - 120 = 840 \, \text{m}^2 \]

### Step 4: Calculate the Length of Wallpaper Required
Given that the width of the wallpaper is 1.2 m, we can find the length of wallpaper needed:
\[ \text{Length of wallpaper} = \frac{\text{Area to be papered}}{\text{Width of wallpaper}} = \frac{840}{1.2} = 700 \, \text{m} \]

### Step 5: Calculate the Cost of Papering
The cost of papering is given as 70 paise per meter. To find the total cost:
\[ \text{Total cost} = \text{Length of wallpaper} \times \text{Cost per meter} = 700 \times 0.70 = 490 \, \text{rupees} \]

### Final Answer
The expenditure of papering the walls is **490 rupees**.

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