Square fencing then inner pavement – Two-step cost: Fencing a square field at Rs 20 per metre costs Rs 10,080. What will it cost to lay a 3 m wide pavement along the inside edge at Rs 50 per sq m?

Introduction / Context:First find square side from fencing cost (perimeter known). Inner pavement forms a border strip of uniform width; its area equals area(outer square) − area(inner square).

Given Data / Assumptions:

• Fencing cost = Rs 10,080 at Rs 20/m ⇒ perimeter P = 10,080 / 20 = 504 m.
• Square perimeter P = 4s ⇒ side s = 504 / 4 = 126 m.
• Pavement width w = 3 m; cost rate = Rs 50/sq m.

Concept / Approach:Area of 3 m wide strip inside = s^2 − (s − 2w)^2 (subtract inner square where each side shrinks by 2w).

Step-by-Step Solution:

Verification / Alternative check:Approx strip area ≈ perimeter * width = 504 * 3 = 1,512 m^2 minus corner corrections (~36) ⇒ 1,476 m^2, consistent.

Why Other Options Are Wrong:43,800 and 53,800 are too low; 83,800 too high; 73,800 matches exact computation.

Common Pitfalls:Using (s − w)^2 instead of (s − 2w)^2; forgetting to derive s from fencing cost.

Final Answer:73800