The length of a rectangular plot is 20 m more than its breadth.\nThe plot is fenced completely around its boundary. The fencing cost is ₹26.50 per metre, and the total fencing cost is ₹5300.\nWhat is the length of the plot in metres?

Introduction:
This problem connects perimeter of a rectangle with a real-life cost scenario (fencing). The fencing cost per metre multiplied by the total perimeter gives the total cost. Once we compute the perimeter, we form an equation using the relationship between length and breadth. Because the length is expressed in terms of breadth (length = breadth + 20), the rectangle has only one unknown, so we can solve using basic algebra. This is a common aptitude question that checks whether you correctly translate a word problem into perimeter equations and handle units and cost conversion accurately.

Given Data / Assumptions:

• Fencing rate = ₹26.50 per metre
• Total fencing cost = ₹5300
• Rectangle perimeter P = total fence length (metres)
• Length L = breadth B + 20
• Perimeter formula: P = 2(L + B)

Concept / Approach:
First compute the perimeter from cost: P = total cost / rate. Then substitute L = B + 20 into P = 2(L + B) to solve for B, and then find L. This is a two-step process: cost-to-perimeter, then perimeter-to-dimensions.

Step-by-Step Solution:
Perimeter P = 5300 / 26.50 = 200 metresSo 2(L + B) = 200 => L + B = 100Given L = B + 20Substitute: (B + 20) + B = 1002B + 20 = 1002B = 80 => B = 40L = B + 20 = 40 + 20 = 60

Verification / Alternative Check:
Check perimeter with L = 60 and B = 40:\nP = 2(60 + 40) = 200 m. Cost = 200 * 26.50 = ₹5300, matches perfectly. The difference L - B = 20 m also matches the statement. This confirms the computed length is correct without any ambiguity.

Why Other Options Are Wrong:
50 m: would imply breadth 30 m and perimeter 160 m, not matching cost.40 m: would imply breadth 20 m and perimeter 120 m, too small.70 m or 80 m: would create perimeter larger than 200 m, exceeding the given cost.

Common Pitfalls:
Multiplying cost instead of dividing to get perimeter.Forgetting perimeter uses 2(L + B), not L + B.Using ₹26.50 incorrectly as 26.05 or 265.Mistake in algebra when substituting L = B + 20.

Final Answer:
60 m