The length of a rectangular plot is 20 m more than its breadth. If 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 perimeter (fencing) with a linear relationship between length and breadth. Fencing a rectangular plot means fencing its boundary, which is the perimeter. The cost information gives the total perimeter because cost = (rate per metre) * (perimeter). Once the perimeter is known, we use the rectangle perimeter formula 2*(L + B). Along with the condition that length is 20 m more than breadth, we can solve for both dimensions. The final question asks only for the length, but we still compute breadth internally as part of solving the system. This is a classic two-step aptitude problem: first convert money to perimeter, then use algebra for rectangle dimensions.

Given Data / Assumptions:

• Length L = B + 20 m
• Fencing rate = Rs 26.50 per m
• Total cost = Rs 5300
• Perimeter P = 2*(L + B)

Concept / Approach:
Compute perimeter from cost: P = 5300 / 26.50. Then use 2*(L+B)=P with L=B+20 to find L.

Step-by-Step Solution:
Perimeter P = Total cost / Rate = 5300 / 26.50 5300 / 26.50 = 200 m So, 2*(L + B) = 200 => L + B = 100 Given L = B + 20 Substitute: (B + 20) + B = 100 => 2B + 20 = 100 2B = 80 => B = 40 L = B + 20 = 40 + 20 = 60 m

Verification / Alternative check:
Check perimeter with L=60 and B=40: 2*(60+40)=2*100=200 m. Cost would be 200*26.50=5300, matching the given cost exactly.

Why Other Options Are Wrong:
40 m is the breadth, not the length. 20 m and 30 m are too small to satisfy both the perimeter and the +20 relation. 50 m would make breadth 30 m, giving L+B=80, not 100.

Common Pitfalls:
Using area instead of perimeter for fencing, forgetting to divide by the fencing rate, or forgetting the factor 2 in the perimeter formula.

Final Answer:
The length of the plot is 60 m.