Step-by-Step Solution

To solve this problem, we can set up algebraic equations based on the perimeters of the two rectangular plots described.

1. Analyze the Larger Rectangular Plot

• Let L be the length and B be the breadth of the original plot.
• The perimeter is given as 100m.
• The formula for perimeter is 2 × (Length + Breadth).
• So, 2(L + B) = 100, which simplifies to L + B = 50.

2. Analyze the Smaller Rectangular Plot

Two friends, A and B, start at diagonally opposite corners and walk to new positions, which become the corners of a smaller rectangle.

• Friend A walks x meters along the length and y meters along the breadth.
• Friend B walks x meters along the breadth and y meters along the length.
• The total reduction in the length of the new plot comes from A's horizontal walk (x) and B's horizontal walk (y). So, the new length is L - x - y.
• Similarly, the total reduction in the breadth of the new plot comes from A's vertical walk (y) and B's vertical walk (x). So, the new breadth is B - x - y.

3. Formulate the Second Equation

The perimeter of the new, smaller plot is 40m.

2 × ((L - x - y) + (B - x - y)) = 40

Dividing by 2, we get:

(L - x - y) + (B - x - y) = 20

Rearranging the terms:

(L + B) - 2(x + y) = 20

4. Solve for the Distance A Walked

We can now substitute the result from the first step (L + B = 50) into our second equation:

50 - 2(x + y) = 20

30 = 2(x + y)

x + y = 15

The total distance A walked is the sum of his horizontal walk (x) and his vertical walk (y).

Conclusion

The total distance A walked is x + y, which is 15 meters.