To solve this problem, we need to understand how the paths are laid out and how to calculate the area of the paths that need leveling.

Step-by-Step Explanation:

1. Rectangular Field Dimensions:

   • Length of the field = 25 meters
   • Width of the field = 18 meters

2. Paths:

   • Two paths are laid perpendicular to each other.
   • Each path is 3 meters wide.
   • One path is parallel to the length, and the other is parallel to the width.

3. Path Dimensions:

   • The path parallel to the length has dimensions:
     $25 \, \text{meters} \, \times \, 3 \, \text{meters}$
   • The path parallel to the width has dimensions:
     $18 \, \text{meters} \, \times \, 3 \, \text{meters}$

4. Overlapping Area: Since the paths are perpendicular, they intersect and overlap at a 3 m x 3 m square. This overlap should not be double-counted, so we will subtract the area of this overlap.

5. Area Calculation:

   • Area of path along the length = $25 \times 3 = 75 \, \text{sq. meters}$
   • Area of path along the width = $18 \times 3 = 54 \, \text{sq. meters}$
   • Overlapping area = $3 \times 3 = 9 \, \text{sq. meters}$

   Now, the total area of the paths is: $\text{Total area} = (75 + 54 - 9) = 120 \, \text{sq. meters}$

6. Cost Calculation: The cost of leveling the path is given as ₹12 per square meter. Therefore, the total cost is: $\text{Cost} = 120 \times 12 = 1440 \, \text{Rupees}$

Diagram Description:

Imagine a rectangular field of 25 meters by 18 meters. There is one 3-meter-wide path running along the length and another 3-meter-wide path running along the width. These paths intersect in the middle, creating an overlap that looks like a small square in the center of the field.

I can also create a visual representation of this layout to help illustrate the problem better.

Let me know if you'd like me to generate the diagram.

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Do you want further details on this solution? Here are 5 related questions:

1. What would be the cost if the paths were 2 meters wide instead of 3 meters?
2. How does the total area of paths change if the field dimensions increase by 10 meters in both length and width?
3. How would the problem change if there were three paths instead of two?
4. How much of the field area remains uncovered by the paths?
5. What would be the cost if the rate per square meter was ₹15 instead of ₹12?

Tip: Always subtract the overlapping area in problems where two paths intersect to avoid double-counting.