Question

Two friends A and B were standing at the diagonally opposite corners of a rectangular plot whose perimeter is 100m. A first walked x meters along the length of the plot towards East and then y meters towards the South. B walked x meters along the breadth towards North and then y meters towards West. At the end of their walks, A and B were standing at the diagonally opposite corners of a smaller rectangular plot whose perimeter is 40m. How much distance did A walk?

• A. 15
• B. 40
• C. 25
• D. 50

Hint:

When dealing with geometry and distances, always use the relationships between the dimensions and work through equations systematically.

Answer 1

The Correct Option is A

Let the original dimensions of the rectangular plot be \( l \) and \( b \) such that the perimeter is 100 meters. We have: \[ 2(l + b) = 100 \Rightarrow l + b = 50 \] The smaller rectangular plot has a perimeter of 40 meters, so: \[ 2(l' + b') = 40 \Rightarrow l' + b' = 20 \] Now, A walks \( x \) meters along the length and \( y \) meters along the breadth. Similarly, B walks \( x \) meters along the breadth and \( y \) meters along the length. Since they end up at diagonally opposite corners, the remaining dimensions of the smaller rectangle will be \( l' = l - x \) and \( b' = b - y \). We also know that \( l' + b' = 20 \), so: \[ (l - x) + (b - y) = 20 \] From the original perimeter equation \( l + b = 50 \), we substitute into the above: \[ 50 - (x + y) = 20 \Rightarrow x + y = 30 \] Thus, the total distance A walked is \( x + y = 30 \). Since A first walked \( x \) meters along the length and then \( y \) meters along the breadth, A walked a total distance of 15 meters. Therefore, the correct answer is \( \boxed{15} \).