A path 3 m wide is running along the inside of the boundary of a rectangular field 116 m by 76 m . How much money is needed to gravel the path at Rs. 42.50 per `m^(2)`?

Answer

To solve the problem, we need to find the area of the path that runs along the inside of the boundary of the rectangular field and then calculate the cost to gravel that path.

### Step-by-Step Solution:

1. **Identify the dimensions of the rectangular field:**
- Length (L) = 116 m
- Width (W) = 76 m

2. **Determine the width of the path:**
- Width of the path = 3 m

3. **Calculate the inner dimensions of the rectangular field after accounting for the path:**
- Inner Length = Outer Length - 2 × Width of the path
- Inner Length = 116 m - 2 × 3 m = 116 m - 6 m = 110 m
- Inner Width = Outer Width - 2 × Width of the path
- Inner Width = 76 m - 2 × 3 m = 76 m - 6 m = 70 m

4. **Calculate the area of the outer rectangle (the whole field):**
- Area of the outer rectangle = Length × Width
- Area of the outer rectangle = 116 m × 76 m = 8816 m²

5. **Calculate the area of the inner rectangle (the area not covered by the path):**
- Area of the inner rectangle = Inner Length × Inner Width
- Area of the inner rectangle = 110 m × 70 m = 7700 m²

6. **Calculate the area of the path:**
- Area of the path = Area of the outer rectangle - Area of the inner rectangle
- Area of the path = 8816 m² - 7700 m² = 1116 m²

7. **Determine the cost to gravel the path:**
- Cost per m² = Rs. 42.50
- Total cost = Area of the path × Cost per m²
- Total cost = 1116 m² × 42.50 Rs/m² = 47430 Rs

### Final Answer:
The total money needed to gravel the path is **Rs. 47430**.