A vendor buys bananas at the rate of 2 for Re 1 and sells them at the rate of 10 for Rs 7. What is his overall profit or loss percentage on the bananas?

Introduction / Context:
This question checks your understanding of unit cost and unit selling price when items are bought and sold in different group sizes. The vendor buys bananas in one ratio (2 for Re 1) and sells them in another ratio (10 for Rs 7). You need to convert both to a common per unit basis to find the profit or loss percentage. Such questions are classic in profit and loss sections of aptitude tests.

Given Data / Assumptions:

• Buying rate: 2 bananas for Re 1.
• Selling rate: 10 bananas for Rs 7.
• We assume no wastage and that all bananas purchased are sold.
• We must find the profit or loss percentage.

Concept / Approach:
The easiest method is to find cost price and selling price per banana:

• CP per banana = total cost / number of bananas when buying.
• SP per banana = total selling price / number of bananas when selling.
• Then profit per banana = SP per banana - CP per banana.
• Profit percentage = (Profit / CP per banana) * 100.

Since the numbers are small and simple, calculations are straightforward.

Step-by-Step Solution:
Step 1: Compute cost price per banana. Step 2: 2 bananas cost Re 1, so CP per banana = 1 / 2 = Rs 0.50. Step 3: Compute selling price per banana. Step 4: 10 bananas sell for Rs 7, so SP per banana = 7 / 10 = Rs 0.70. Step 5: Profit per banana = SP - CP = 0.70 - 0.50 = Rs 0.20. Step 6: Profit percentage = (0.20 / 0.50) * 100. Step 7: 0.20 / 0.50 = 0.4. Step 8: Profit percentage = 0.4 * 100 = 40%.

Verification / Alternative check:
Consider buying and selling the same number of bananas, for example 10 bananas:

• To buy 10 bananas at 2 for Re 1: for every 2 bananas, cost is Re 1, so 10 bananas cost 5 rupees.
• To sell 10 bananas at the given selling rate: 10 bananas sell for Rs 7.
• Profit on 10 bananas = 7 - 5 = Rs 2.
• Cost price of 10 bananas = Rs 5, profit percentage = 2 / 5 * 100 = 40%.

This check confirms the same answer using a batch approach instead of per-unit calculations.

Why Other Options Are Wrong:
40 percent loss: Incorrect because selling price per banana (Rs 0.70) is clearly higher than cost price (Rs 0.50).
28.57 percent gain: This percentage often comes from mixing up ratios, but does not match the computed profit ratio of 0.4.
28.5 percent loss: Also clearly wrong because there is a gain, not a loss.
Only 40 percent gain matches both per unit and batch-based calculations exactly.

Common Pitfalls:
A common mistake is to compare the total buy and sell numbers directly without adjusting for quantity, for example comparing 2 for 1 with 10 for 7 in a confusing way. Always convert both rates to the same base, usually cost and selling price per single unit or for a common number of units like 10 or 20. Careless handling of decimal values like 0.5 and 0.7 can also cause errors, so work slowly and check your arithmetic.

Final Answer:
The vendor makes a 40 percent gain on the bananas.