A street vendor buys bananas at a rate of 7 bananas for Rs 6 and sells them at a rate of 6 bananas for Rs 7. What is his overall percentage profit or loss?

Introduction / Context:
This is a classic type of profit and loss question involving selling items by different count based rates instead of directly by unit price. The vendor buys bananas at one rate and sells them at another, and we must compute the percentage profit or loss. These problems are very common in competitive exams and require converting both buying and selling terms into per unit costs and then comparing them.

Given Data / Assumptions:

• Purchase rate: 7 bananas for Rs 6.
• Selling rate: 6 bananas for Rs 7.
• All bananas are identical and there is no wastage.
• We need to find the overall percentage profit or loss.

Concept / Approach:
We calculate:

• Cost price per banana = total cost / number of bananas bought.
• Selling price per banana = total selling amount / number of bananas sold.
• Profit or loss per banana = selling price per banana minus cost price per banana.
• Profit percent = (profit per banana / cost price per banana) * 100.

The same percentage will apply regardless of the total number sold due to linearity.

Step-by-Step Solution:
Cost for 7 bananas = Rs 6. Cost price per banana = 6 / 7 rupees. Selling price for 6 bananas = Rs 7. Selling price per banana = 7 / 6 rupees. Profit per banana = SP - CP = (7 / 6) - (6 / 7). Compute difference: (7 / 6) - (6 / 7) = (49 / 42) - (36 / 42) = 13 / 42. Cost price per banana = 6 / 7 = 36 / 42. Profit percent = (profit / cost) * 100 = (13 / 42) / (36 / 42) * 100. This simplifies to (13 / 36) * 100 ≈ 36.11%. Therefore, the vendor makes approximately 36.1% profit.

Verification / Alternative check:
Consider buying 42 bananas, a common multiple of 7 and 6:

• To get 42 bananas, the vendor buys 6 batches of 7 bananas.
• Total cost = 6 * 6 = Rs 36.
• He then sells 42 bananas in batches of 6 bananas each, that is 7 batches.
• Total revenue = 7 * 7 = Rs 49.
• Profit = 49 - 36 = Rs 13.
• Profit percent = (13 / 36) * 100 ≈ 36.11%.

This matches the earlier calculation, confirming the answer.

Why Other Options Are Wrong:
Options claiming loss are impossible because the selling price per banana is clearly higher than the cost price per banana. A profit of 26.5% or 43.75% does not match the exact ratio of revenue to cost in this scheme. The accurate profit percent is about 36.1%, so the closest and correct option is 36.1% profit.

Common Pitfalls:
Many students mistakenly compare 7 and 6 directly without converting to per unit values. Others may invert the rate and treat 7 bananas for Rs 6 as Rs 7 for 6 bananas, leading to incorrect calculations. Always convert such rate problems to cost and selling price per single unit before computing percentages.

Final Answer:
The vendor makes a 36.1% profit on selling the bananas.