A rectangular grassy land is 65 m long and 50 m broad . It is surrounded by 3 m wide path . Find the cost of gravelling the path at Rs 2.50 per `m^(2)`.

Options

A. Rs. 1500
B. Rs. 1518
C. Rs. 1815
D. Rs. 1960

Answer

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

### Step 1: Find the dimensions of the larger rectangle (including the path).
- The original grassy land is 65 m long and 50 m wide.
- The path surrounding the grassy land is 3 m wide on all sides.
- Therefore, the length of the larger rectangle will be:
\[ \text{Length} = 65 \, \text{m} + 2 \times 3 \, \text{m} = 65 \, \text{m} + 6 \, \text{m} = 71 \, \text{m} \]
- The width of the larger rectangle will be:
\[ \text{Width} = 50 \, \text{m} + 2 \times 3 \, \text{m} = 50 \, \text{m} + 6 \, \text{m} = 56 \, \text{m} \]

### Step 2: Calculate the area of the larger rectangle.
- The area of the larger rectangle is given by:
\[ \text{Area}_{\text{larger}} = \text{Length} \times \text{Width} = 71 \, \text{m} \times 56 \, \text{m} = 3976 \, \text{m}^2 \]

### Step 3: Calculate the area of the grassy land.
- The area of the grassy land is:
\[ \text{Area}_{\text{grassy}} = \text{Length} \times \text{Width} = 65 \, \text{m} \times 50 \, \text{m} = 3250 \, \text{m}^2 \]

### Step 4: Calculate the area of the path.
- The area of the path is the difference between the area of the larger rectangle and the area of the grassy land:
\[ \text{Area}_{\text{path}} = \text{Area}_{\text{larger}} - \text{Area}_{\text{grassy}} = 3976 \, \text{m}^2 - 3250 \, \text{m}^2 = 726 \, \text{m}^2 \]

### Step 5: Calculate the cost of gravelling the path.
- The cost of gravelling is given as Rs 2.50 per square meter. Therefore, the total cost is:
\[ \text{Cost} = \text{Area}_{\text{path}} \times \text{Cost per m}^2 = 726 \, \text{m}^2 \times 2.50 \, \text{Rs/m}^2 = 1815 \, \text{Rs} \]

### Final Answer:
The cost of gravelling the path is **Rs 1815**.