A rectangular 75 m by 60 m has a `1.5 m` wide path runing around outside it. Find the cost gravelling this path at the rate of Rs 8 per sq. m

Answer

To solve the problem step by step, we will follow the outlined process to find the cost of gravelling the path around the rectangular area.

### Step 1: Calculate the area of the original rectangle.
The dimensions of the rectangle are given as:
- Length = 75 m
- Breadth = 60 m

The area of the rectangle (A) can be calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
So,
\[ \text{Area} = 75 \, \text{m} \times 60 \, \text{m} = 4500 \, \text{m}^2 \]

### Step 2: Calculate the new dimensions of the rectangle including the path.
The path is 1.5 m wide and runs around the outside of the rectangle. Therefore, we need to add this width to both sides of the length and breadth.

- New Length = Original Length + 1.5 m (on one side) + 1.5 m (on the other side)
\[ \text{New Length} = 75 \, \text{m} + 1.5 \, \text{m} + 1.5 \, \text{m} = 78 \, \text{m} \]

- New Breadth = Original Breadth + 1.5 m (on one side) + 1.5 m (on the other side)
\[ \text{New Breadth} = 60 \, \text{m} + 1.5 \, \text{m} + 1.5 \, \text{m} = 63 \, \text{m} \]

### Step 3: Calculate the area of the new rectangle including the path.
Now we calculate the area of the new rectangle (P Q R S) using the new dimensions:
\[ \text{Area of P Q R S} = \text{New Length} \times \text{New Breadth} \]
So,
\[ \text{Area of P Q R S} = 78 \, \text{m} \times 63 \, \text{m} = 4914 \, \text{m}^2 \]

### Step 4: Calculate the area of the path.
The area of the path is the difference between the area of the new rectangle and the area of the original rectangle:
\[ \text{Area of Path} = \text{Area of P Q R S} - \text{Area of A B C D} \]
So,
\[ \text{Area of Path} = 4914 \, \text{m}^2 - 4500 \, \text{m}^2 = 414 \, \text{m}^2 \]

### Step 5: Calculate the cost of gravelling the path.
The cost of gravelling is given at the rate of Rs 8 per square meter. Therefore, the total cost can be calculated as:
\[ \text{Cost} = \text{Area of Path} \times \text{Cost per sq. m} \]
So,
\[ \text{Cost} = 414 \, \text{m}^2 \times 8 \, \text{Rs/m}^2 = 3312 \, \text{Rs} \]

### Final Answer:
The cost of gravelling the path is Rs 3312.

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