A rectangular garden is 120 m long and 65 m broad .A path of uniform width of 5 m has to be constructed around it on its outside .Find the cost of gravelling the path at Rs. 11.40 per `m^(2)`.

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Identify the dimensions of the garden and the path
The garden is rectangular with:
- Length = 120 m
- Breadth = 65 m
- Width of the path = 5 m

### Step 2: Calculate the outer dimensions of the garden including the path
Since the path is constructed around the garden, we need to add the width of the path to both sides of the length and breadth.

- Outer Length = Inner Length + 2 × Width of Path
\[ \text{Outer Length} = 120 \, \text{m} + 2 \times 5 \, \text{m} = 120 \, \text{m} + 10 \, \text{m} = 130 \, \text{m} \]

- Outer Breadth = Inner Breadth + 2 × Width of Path
\[ \text{Outer Breadth} = 65 \, \text{m} + 2 \times 5 \, \text{m} = 65 \, \text{m} + 10 \, \text{m} = 75 \, \text{m} \]

### Step 3: Calculate the area of the outer rectangle (garden + path)
Using the formula for the area of a rectangle (Area = Length × Breadth):
\[ \text{Area of Outer Rectangle} = \text{Outer Length} \times \text{Outer Breadth} = 130 \, \text{m} \times 75 \, \text{m} = 9750 \, \text{m}^2 \]

### Step 4: Calculate the area of the inner rectangle (the garden)
\[ \text{Area of Inner Rectangle} = \text{Inner Length} \times \text{Inner Breadth} = 120 \, \text{m} \times 65 \, \text{m} = 7800 \, \text{m}^2 \]

### Step 5: Calculate the area of the path
The area of the path is the difference between the area of the outer rectangle and the area of the inner rectangle:
\[ \text{Area of Path} = \text{Area of Outer Rectangle} - \text{Area of Inner Rectangle} = 9750 \, \text{m}^2 - 7800 \, \text{m}^2 = 1950 \, \text{m}^2 \]

### Step 6: Calculate the cost of gravelling the path
The cost of gravelling is given at Rs. 11.40 per square meter. Therefore, the total cost is:
\[ \text{Cost} = \text{Area of Path} \times \text{Cost per m}^2 = 1950 \, \text{m}^2 \times 11.40 \, \text{Rs/m}^2 = 22,230 \, \text{Rs} \]

### Final Answer:
The cost of gravelling the path is **Rs. 22,230**.

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