To solve the problem step by step, we will find the area of the cross paths and then calculate the cost of gravelling them.
### Step 1: Understand the dimensions of the lawn and paths
- The lawn is rectangular with a length of 115 m and a breadth of 64 m.
- There are two cross paths:
- One path is 2 m wide and runs parallel to the length (115 m).
- The other path is 2.5 m wide and runs parallel to the breadth (64 m).
### Step 2: Calculate the area of the first path
- The area of the first path (which runs parallel to the length) can be calculated using the formula for the area of a rectangle:
\[
\text{Area of first path} = \text{Length} \times \text{Width} = 115 \, \text{m} \times 2 \, \text{m} = 230 \, \text{m}^2
\]
### Step 3: Calculate the area of the second path
- The area of the second path (which runs parallel to the breadth) is calculated similarly:
\[
\text{Area of second path} = \text{Length} \times \text{Width} = 64 \, \text{m} \times 2.5 \, \text{m} = 160 \, \text{m}^2
\]
### Step 4: Calculate the area of the common part
- The common area where both paths overlap must be subtracted from the total area. This common area is a rectangle formed by the widths of both paths:
\[
\text{Common area} = \text{Width of first path} \times \text{Width of second path} = 2 \, \text{m} \times 2.5 \, \text{m} = 5 \, \text{m}^2
\]
### Step 5: Calculate the total area of the paths
- Now, we can find the total area of the paths by adding the areas of the two paths and subtracting the common area:
\[
\text{Total area of paths} = \text{Area of first path} + \text{Area of second path} - \text{Common area}
\]
\[
= 230 \, \text{m}^2 + 160 \, \text{m}^2 - 5 \, \text{m}^2 = 385 \, \text{m}^2
\]
### Step 6: Calculate the cost of gravelling the paths
- The cost of gravelling is given as Rs. 114 per square meter. Therefore, the total cost can be calculated as:
\[
\text{Total cost} = \text{Cost per m}^2 \times \text{Total area of paths}
\]
\[
= 114 \, \text{Rs/m}^2 \times 385 \, \text{m}^2 = 43,890 \, \text{Rs}
\]
### Final Answer
The cost of gravelling the paths is Rs. 43,890.
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