A vendor buys 6 bananas for Rs 25 and sells them at a rate of 3 bananas for Rs 20. What is his profit percentage on this transaction?

Introduction / Context:
This profit and loss question again involves unit prices derived from batch buying and selling. The vendor buys bananas in one quantity and sells them in smaller packs at a different rate. To find profit percentage, we must compare cost price per banana and selling price per banana.

Given Data / Assumptions:
- Cost of 6 bananas = Rs 25. - Selling price of 3 bananas = Rs 20. - All bananas are identical and there is no wastage. - The vendor sells all bananas at the given rate.

Concept / Approach:
We find cost price per banana and selling price per banana, then compute profit per banana and profit percentage on cost price. The formulas used are:
cost per banana = total cost / number of bananas bought selling price per banana = pack selling price / bananas per pack profit per banana = selling price per banana - cost per banana profit percent = (profit per banana / cost per banana) * 100

Step-by-Step Solution:
Step 1: Cost price for 6 bananas = Rs 25. Step 2: Cost price per banana = 25 / 6 ≈ Rs 4.1667. Step 3: Selling price for 3 bananas = Rs 20. Step 4: Selling price per banana = 20 / 3 ≈ Rs 6.6667. Step 5: Profit per banana ≈ 6.6667 - 4.1667 = Rs 2.5. Step 6: Profit percent = (2.5 / (25 / 6)) * 100 = (2.5 * 6 / 25) * 100 = 0.6 * 100 = 60%.

Verification / Alternative check:
Consider 6 bananas as a whole batch. Cost price = Rs 25. The vendor sells 6 bananas as two packs of 3 bananas. Each pack sells for Rs 20, so total selling price for 6 bananas = 2 * 20 = Rs 40. Profit on the batch = 40 - 25 = Rs 15. Profit percent = 15 / 25 * 100 = 60%. This matches the per banana calculation.

Why Other Options Are Wrong:
Option 50 would require a profit of Rs 12.5 on a cost of 25, which does not fit the selling rate. Option 40 and 30 are lower than the correct profit percentage and come from errors such as using wrong unit prices or dividing by selling price instead of cost price.

Common Pitfalls:
Some learners incorrectly compute profit percentage as profit divided by selling price, or they confuse the cost of 3 bananas with the cost of 6. It is also easy to forget to convert both buying and selling situations to a common number of bananas before comparing. Always align the quantities before applying percentage formulas.

Final Answer:
The vendor's profit percentage is 60%.