The length of a rectangular plot is 20 metres more than its breadth. The cost of fencing the plot at Rs 26.50 per metre is Rs 5300. What is the length of the plot (in metres)?

Introduction / Context:
This question combines basic algebra with the concept of perimeter of a rectangle and cost calculation. The fencing cost is given per metre, and the total cost is known. Using this information, we can find the total length of fencing, which is the perimeter. Then, with the relationship between length and breadth, we can determine the actual dimensions of the rectangular plot. This type of problem is common in aptitude tests and practical planning scenarios such as estimating construction or fencing costs.

Given Data / Assumptions:
• Let the breadth of the rectangular plot be b metres.
• Then the length of the plot is b + 20 metres, since it is 20 m more than the breadth.
• Fencing is done around the entire boundary, so the total fenced length equals the perimeter of the rectangle.
• Cost of fencing is Rs 26.50 per metre.
• Total fencing cost is Rs 5300.

Concept / Approach:
The perimeter P of a rectangle with length L and breadth B is given by P = 2(L + B). The total cost is cost per metre multiplied by the perimeter. Therefore, we can write 26.50 * P = 5300. Solving for P gives the total perimeter. Next, using the relationship between length and breadth, we can set up an equation and solve for b. From b we then find the length L = b + 20. This approach is systematic and uses only basic algebra.

Step-by-Step Solution:
Step 1: Let breadth = b metres and length = b + 20 metres. Step 2: Perimeter P of the rectangle is P = 2(L + B) = 2[(b + 20) + b] = 2(2b + 20) = 4b + 40. Step 3: Cost of fencing is Rs 26.50 per metre, so total cost is 26.50 * P. Step 4: Given total cost equals Rs 5300, we have 26.50 * (4b + 40) = 5300. Step 5: Divide both sides by 26.50 to find the perimeter: 4b + 40 = 5300 / 26.50 = 200. Step 6: Solve 4b + 40 = 200 to get 4b = 160, so b = 40 metres. Step 7: The length is then L = b + 20 = 40 + 20 = 60 metres.

Verification / Alternative check:
With breadth 40 metres and length 60 metres, the perimeter is P = 2(60 + 40) = 2 * 100 = 200 metres. At a rate of Rs 26.50 per metre, the total cost is 26.50 * 200 = 5300 rupees, which matches the given cost. This confirms that the dimensions are consistent with the information provided. Any other combination of length and breadth related by a 20 metre difference would yield a different perimeter and therefore a different cost.

Why Other Options Are Wrong:
40 metres would mean the length equals the breadth, violating the condition that length is 20 metres more than breadth.
50, 80, and 120 metres do not satisfy the equation 4b + 40 = 200 when combined with an appropriate breadth and also do not produce the fencing cost of Rs 5300 at Rs 26.50 per metre. Only 60 metres leads to a perimeter of 200 metres and the correct total cost.

Common Pitfalls:
Learners sometimes confuse perimeter with area and try to use the cost to find area instead of the boundary length. Another common mistake is to mis-handle the relationship between length and breadth, for example setting length = 20b instead of b + 20. Arithmetic errors can also occur when dividing 5300 by 26.50. Writing down each relation clearly and performing the division carefully ensures the correct answer.

Final Answer:
The length of the rectangular plot is 60 metres.