A rectangular garden 63 m long and 54 m broad has a path 3m wide inside it . Find the cost of paving the path ar Rs. 37/2 per square metre :

Options

A. Rs. 12321
B. Rs. 11100
C. Rs. 74000
D. none of these

Answer

To solve the problem step by step, we will calculate the area of the rectangular garden, the area of the path, and then find the cost of paving the path.

### Step 1: Calculate the area of the rectangular garden.
The area of a rectangle is calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]

Given:
- Length = 63 m
- Breadth = 54 m

Calculating the area:
\[ \text{Area of the garden} = 63 \, \text{m} \times 54 \, \text{m} = 3402 \, \text{m}^2 \]

### Step 2: Calculate the dimensions of the inner rectangle (the area without the path).
Since there is a path of 3 m wide inside the garden, we need to subtract 3 m from each side of the length and breadth.

New dimensions:
- New Length = \( 63 \, \text{m} - 2 \times 3 \, \text{m} = 63 \, \text{m} - 6 \, \text{m} = 57 \, \text{m} \)
- New Breadth = \( 54 \, \text{m} - 2 \times 3 \, \text{m} = 54 \, \text{m} - 6 \, \text{m} = 48 \, \text{m} \)

Calculating the area of the inner rectangle:
\[ \text{Area of the inner rectangle} = 57 \, \text{m} \times 48 \, \text{m} = 2736 \, \text{m}^2 \]

### Step 3: Calculate the area of the path.
The area of the path is the difference between the area of the garden and the area of the inner rectangle:
\[ \text{Area of the path} = \text{Area of the garden} - \text{Area of the inner rectangle} \]
\[ \text{Area of the path} = 3402 \, \text{m}^2 - 2736 \, \text{m}^2 = 666 \, \text{m}^2 \]

### Step 4: Calculate the cost of paving the path.
The cost of paving is given as Rs. \( \frac{37}{2} \) per square meter.

Calculating the total cost:
\[ \text{Total Cost} = \text{Area of the path} \times \text{Cost per square meter} \]
\[ \text{Total Cost} = 666 \, \text{m}^2 \times \frac{37}{2} = 666 \times 18.5 = 12321 \, \text{Rs} \]

### Final Answer:
The cost of paving the path is **Rs. 12321**.

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