A hall 25 metres long and 15 metres broad is surrounded by a verandah of uniform width of 3.5 metres. The cost of flooring the verandah, at Rs. 27.50 per square metre is

Options

A. Rs. 9149.50
B. Rs. 8146.50
C. Rs. 9047.50
D. Rs. 4186.50

Answer

To solve the problem, we need to find the area of the verandah surrounding the hall and then calculate the cost of flooring that area. Here’s the step-by-step solution:

### Step 1: Find the dimensions of the hall
The hall is given to be:
- Length = 25 meters
- Breadth = 15 meters

### Step 2: Calculate the dimensions of the outer rectangle (hall + verandah)
The verandah has a uniform width of 3.5 meters on all sides. Therefore, we need to add twice the width of the verandah to both the length and the breadth of the hall.

- Outer Length = Length of hall + 2 × Width of verandah
\[ \text{Outer Length} = 25 + 2 \times 3.5 = 25 + 7 = 32 \text{ meters} \]

- Outer Breadth = Breadth of hall + 2 × Width of verandah
\[ \text{Outer Breadth} = 15 + 2 \times 3.5 = 15 + 7 = 22 \text{ meters} \]

### Step 3: Calculate the area of the outer rectangle (hall + verandah)
Now, we calculate the area of the outer rectangle:
\[ \text{Area of outer rectangle} = \text{Outer Length} \times \text{Outer Breadth} = 32 \times 22 = 704 \text{ square meters} \]

### Step 4: Calculate the area of the hall
Next, we calculate the area of the hall:
\[ \text{Area of hall} = \text{Length} \times \text{Breadth} = 25 \times 15 = 375 \text{ square meters} \]

### Step 5: Calculate the area of the verandah
The area of the verandah is the area of the outer rectangle minus the area of the hall:
\[ \text{Area of verandah} = \text{Area of outer rectangle} - \text{Area of hall} = 704 - 375 = 329 \text{ square meters} \]

### Step 6: Calculate the cost of flooring the verandah
The cost of flooring is given as Rs. 27.50 per square meter. Therefore, the total cost can be calculated as follows:
\[ \text{Cost} = \text{Area of verandah} \times \text{Cost per square meter} = 329 \times 27.50 \]
Calculating this gives:
\[ \text{Cost} = 9047.50 \text{ Rs.} \]

### Final Answer
The cost of flooring the verandah is **Rs. 9047.50**.

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