The cost of fencing a square field at ₹20 per metre is ₹10,080. A 3 metre wide pavement is to be laid all along the inside of the fencing (uniform width on all four sides). Find the total cost of laying this pavement at ₹50 per sq m, assuming the pavement covers only the ring-shaped area between the outer square and the inner square.

Introduction / Context:This question tests a two-step mensuration process. First, you use fencing cost to find the square’s perimeter and side. Second, you compute the area of an inside pavement strip of uniform width, which forms a “square ring”: area of outer square minus area of inner square. Finally, convert the pavement area into cost using the given rate per square metre.

Given Data / Assumptions:

• Fencing rate = ₹20 per metre
• Total fencing cost = ₹10,080
• Square perimeter = total cost / rate
• Pavement width inside = 3 m on each side
• Pavement rate = ₹50 per sq m

Concept / Approach:Find side of outer square from perimeter. Inner square side = outer side - 2*width. Pavement area = outer side^2 - inner side^2. Cost = area * 50.

Step-by-Step Solution:

Verification / Alternative check:Width is 3 m on all sides, so subtracting 6 m from the side is correct. The pavement area should be noticeably smaller than the full field area 126^2, and 1476 sq m is a reasonable “ring” area. Multiplying by ₹50 gives ₹73,800, consistent in magnitude.

Why Other Options Are Wrong:

Common Pitfalls:Common mistakes include treating ₹10,080 as perimeter directly, forgetting the rate ₹20 per metre, computing inner side as 126 - 3 (instead of 126 - 6), or using 2*(126+120)*3 as area without understanding the ring method. The ring method (difference of squares) is clean and reliable here.

Final Answer:₹73,800