The cost of fencing a rectangular field at Rs. 7.50 per metre is Rs. 600. If its length is 24 m, find its breadth :

Question

Accepted Answer

To determine the breadth of the rectangular field, we need to use the information provided about the cost of fencing and the dimensions of the field.

1. **Understanding the Problem:**
   - The cost of fencing the field is Rs. 600 at a rate of Rs. 7.50 per metre.
   - The length of the field is given as 24 metres.
   - We need to find the breadth of the field.

2. **Calculating the Perimeter:**
   - The total cost of fencing is Rs. 600, and the cost per metre is Rs. 7.50.
   - Therefore, the total length of the fence (perimeter of the field) can be calculated as:
     $$
     \text{Perimeter} = \frac{\text{Total Cost}}{\text{Cost per metre}} = \frac{600}{7.50} = 80 \text{ metres}
     $$

3. **Using the Perimeter to Find the Breadth:**
   - The formula for the perimeter of a rectangle is:
     $$
     \text{Perimeter} = 2 \times (\text{Length} + \text{Breadth})
     $$
   - We know the perimeter is 80 metres and the length is 24 metres. Plug these values into the formula:
     $$
     80 = 2 \times (24 + \text{Breadth})
     $$
   - Simplify and solve for the breadth:
     $$
     80 = 48 + 2 \times \text{Breadth}
     $$
     $$
     80 - 48 = 2 \times \text{Breadth}
     $$
     $$
     32 = 2 \times \text{Breadth}
     $$
     $$
     \text{Breadth} = \frac{32}{2} = 16 \text{ metres}
     $$

4. **Conclusion:**
   - The calculated breadth of the field is 16 metres, which matches Option 1.

5. **Explanation of Incorrect Options:**
   - **Option 2 (16.8 m):** If the breadth were 16.8 metres, the perimeter would be $2 \times (24 + 16.8) = 81.6$ metres, which does not match the calculated perimeter of 80 metres.
   - **Option 3 (20 m):** If the breadth were 20 metres, the perimeter would be $2 \times (24 + 20) = 88$ metres, which exceeds the calculated perimeter.
   - **Option 4 (20.8 m):** If the breadth were 20.8 metres, the perimeter would be $2 \times (24 + 20.8) = 89.6$ metres, which also exceeds the calculated perimeter.

Therefore, Option 1 is the correct answer, as it is the only option that satisfies the given conditions and calculations.