The length and breadth of a rectangular piece of land are in the ratio 5 : 3. The owner spends Rs. 6000 on fencing it from all sides at the rate of Rs. 7.50 per metre. What is the difference (in metres) between the length and the breadth of the land?

Introduction / Context:
This is a standard aptitude question involving perimeter of a rectangle, ratios, and unit cost. You are given the total cost of fencing and the rate per metre, and from that you can find the perimeter. The ratio of length to breadth then allows you to find the actual dimensions and hence the difference between length and breadth.

Given Data / Assumptions:
• Ratio of length to breadth is 5 : 3.
• Total fencing cost is Rs. 6000.
• Fencing rate is Rs. 7.50 per metre.
• Shape is a rectangle whose perimeter equals the fenced length.

Concept / Approach:
Let length be 5k and breadth be 3k. The perimeter P of a rectangle is P = 2(length + breadth) = 2(5k + 3k) = 16k. From cost = rate × length of fencing, we first find P, then solve for k. Once k is known, we find length and breadth and their difference.

Step-by-Step Solution:
Step 1: Total fenced length is the perimeter P. Use cost = rate × perimeter. Step 2: Perimeter P = cost / rate = 6000 / 7.50. Step 3: Compute 6000 / 7.5 = 800 metres, so P = 800 m. Step 4: Let length L = 5k and breadth B = 3k. Then P = 2(L + B) = 2(5k + 3k) = 16k. Step 5: Set 16k = 800, so k = 800 / 16 = 50. Step 6: Length L = 5k = 5 × 50 = 250 metres. Step 7: Breadth B = 3k = 3 × 50 = 150 metres. Step 8: Difference between length and breadth = L − B = 250 − 150 = 100 metres.

Verification / Alternative check:
Verify that these dimensions give the correct perimeter and cost. Perimeter = 2(250 + 150) = 2 × 400 = 800 metres. At Rs. 7.50 per metre, cost = 800 × 7.50 = 6000, which matches the given amount. This confirms the calculations.

Why Other Options Are Wrong:
• 50 metres would correspond to k itself and not to the difference L − B.
• 150 metres would incorrectly use only one side or misinterpret the ratio.
• 250 metres is the length, not the difference, and comes from ignoring the breadth.

Common Pitfalls:
A typical mistake is to compute area instead of perimeter, or to forget that fencing is done around all sides, not just length or breadth. Another pitfall is dividing cost by the wrong rate or misusing the 5 : 3 ratio. Writing all steps clearly helps avoid confusion.

Final Answer:
The difference between the length and the breadth is 100 metres.