A hall 20 m long and 15 m broad is surrounded by a verandah of uniform width of 2.5 m. The cost of flooring the verandah at the rate of ₹3.50 per sq. metre is -----

Options

A. ₹500
B. ₹600
C. ₹700
D. ₹800

Answer

To solve the problem step by step, we need to calculate the area of the verandah and then find the cost of flooring it. Here’s how we can do it:

### Step 1: Determine the dimensions of the hall
The dimensions of the hall are given as:
- Length = 20 m
- Breadth = 15 m

### Step 2: Calculate the dimensions of the outer rectangle (including the verandah)
The verandah surrounds the hall uniformly with a width of 2.5 m on all sides. Therefore, we need to add twice the width of the verandah to each dimension of the hall.

- Length of the outer rectangle (PQ) = Length of the hall + 2 × Width of the verandah
\[ PQ = 20 \, \text{m} + 2 \times 2.5 \, \text{m} = 20 + 5 = 25 \, \text{m} \]

- Breadth of the outer rectangle (QR) = Breadth of the hall + 2 × Width of the verandah
\[ QR = 15 \, \text{m} + 2 \times 2.5 \, \text{m} = 15 + 5 = 20 \, \text{m} \]

### Step 3: Calculate the area of the outer rectangle (verandah + hall)
The area of the outer rectangle (PQRS) can be calculated using the formula for the area of a rectangle:
\[ \text{Area}_{PQRS} = \text{Length} \times \text{Breadth} = PQ \times QR = 25 \, \text{m} \times 20 \, \text{m} = 500 \, \text{m}^2 \]

### Step 4: Calculate the area of the hall (ABCD)
The area of the hall can also be calculated using the same formula:
\[ \text{Area}_{ABCD} = \text{Length} \times \text{Breadth} = 20 \, \text{m} \times 15 \, \text{m} = 300 \, \text{m}^2 \]

### Step 5: Calculate the area of the verandah
The area of the verandah can be found by subtracting the area of the hall from the area of the outer rectangle:
\[ \text{Area}_{\text{Verandah}} = \text{Area}_{PQRS} - \text{Area}_{ABCD} = 500 \, \text{m}^2 - 300 \, \text{m}^2 = 200 \, \text{m}^2 \]

### Step 6: Calculate the cost of flooring the verandah
The cost of flooring is given as ₹3.50 per square meter. Therefore, the total cost can be calculated as:
\[ \text{Cost} = \text{Area}_{\text{Verandah}} \times \text{Cost per sq. m} = 200 \, \text{m}^2 \times 3.50 \, \text{₹/m}^2 = 700 \, \text{₹} \]

### Final Answer
The cost of flooring the verandah is **₹700**.

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