The length of a rectangular plot is 20 metres more than its breadth. The cost of fencing the plot at ₹26.50 per metre is ₹5300. Find the length of the plot in metres.

Introduction / Context:
This is a perimeter and cost based problem involving a rectangle. You are given the fencing cost per metre and total cost, from which you can deduce the perimeter. The relationship between length and breadth is specified, so you can set up simple equations to find the dimensions of the plot, particularly the length.

Given Data / Assumptions:

• Let breadth of plot = b metres
• Length of plot = b + 20 metres
• Cost of fencing per metre = ₹26.50
• Total cost of fencing = ₹5300
• Perimeter P of rectangle = 2 * (length + breadth)

Concept / Approach:
First compute the perimeter from the cost information: perimeter = total cost divided by rate per metre. Then express perimeter in terms of b using the rectangle formula. Solving the resulting linear equation gives breadth, and adding 20 gives length. This is a standard algebraic application of perimeter and linear relationships between length and breadth.

Step-by-Step Solution:
Total fencing cost = ₹5300 Rate per metre = ₹26.50 Perimeter P = 5300 / 26.5 P = 200 metres Perimeter of rectangle P = 2 * (length + breadth) 2 * ( (b + 20) + b ) = 200 2 * (2b + 20) = 200 4b + 40 = 200 4b = 160 ⇒ b = 40 metres Length = b + 20 = 40 + 20 = 60 metres

Verification / Alternative check:
If breadth is 40 m and length is 60 m, then perimeter = 2 * (60 + 40) = 2 * 100 = 200 m. Fencing cost = 200 * 26.50 = ₹5300, which matches the given cost exactly. This confirms that the dimensions and the length value 60 m are correct.

Why Other Options Are Wrong:
40 m: This is the breadth, not the length. 50 m: Does not satisfy the 20 metre difference when combined with a valid breadth. 10 m: Far too small and inconsistent with the perimeter. 80 m: Would lead to an incorrect perimeter and fencing cost.

Common Pitfalls:
Forgetting to divide total cost by rate to get the perimeter. Incorrectly forming the perimeter equation from length and breadth. Arithmetic errors while solving the linear equation for b.

Final Answer:
The length of the plot is 60 metres