A vendor buys bananas at a rate of 4 for Rs 3 and sells them at a rate of 3 for Rs 4. What is his overall percentage profit or loss?

Introduction / Context:
This question is similar to other rate based profit and loss problems where items are bought and sold in groups rather than by direct unit price. The vendor purchases bananas at one grouped rate and sells them at another. We need to compute his overall percentage profit or loss. The key is to convert both rates into per unit prices and then compare them.

Given Data / Assumptions:

• Buying rate: 4 bananas for Rs 3.
• Selling rate: 3 bananas for Rs 4.
• No bananas are wasted or spoiled.
• All bananas are identical.
• We must find the percentage profit or loss for the vendor.

Concept / Approach:
Compute:

• Cost price per banana = total cost / number of bananas in buying batch.
• Selling price per banana = total selling amount / number of bananas in selling batch.
• Then find profit per banana and divide by cost price per banana to get profit percent.

The percentage result will be the same irrespective of total number of bananas sold due to proportionality.

Step-by-Step Solution:
Cost for 4 bananas = Rs 3. Cost price per banana = 3 / 4 rupees. Selling price for 3 bananas = Rs 4. Selling price per banana = 4 / 3 rupees. Profit per banana = SP - CP = (4 / 3) - (3 / 4). Compute difference: (4 / 3) - (3 / 4) = (16 / 12) - (9 / 12) = 7 / 12. Cost price per banana = 3 / 4 = 9 / 12. Profit percent = (profit / cost) * 100 = (7 / 12) / (9 / 12) * 100. This simplifies to (7 / 9) * 100 ≈ 77.78%. Thus, the vendor makes approximately 77.7% profit.

Verification / Alternative check:
Consider a convenient total such as 36 bananas, which is the least common multiple of 4 and 3:

• To buy 36 bananas, the vendor buys 9 batches of 4 bananas.
• Total cost = 9 * 3 = Rs 27.
• To sell 36 bananas, he sells 12 batches of 3 bananas.
• Total revenue = 12 * 4 = Rs 48.
• Profit = 48 - 27 = Rs 21.
• Profit percent = (21 / 27) * 100 = 77.78%.

This confirms our earlier calculation.

Why Other Options Are Wrong:
43.75% profit corresponds to a different buying and selling pattern, not this one. Any loss options are impossible because selling price per banana is clearly higher than the cost price per banana. Hence 77.7% loss and 43.75% loss are incorrect. The only option that matches the calculated 77.7% value is 77.7% profit.

Common Pitfalls:
Errors often come from reversing buying and selling rates or from incorrect fraction operations. Some students compare 4 and 3 directly without converting to a per unit basis. Others may mistakenly treat 4 for 3 and 3 for 4 as symmetric and assume no profit or loss. Always compute cost price per unit and selling price per unit first, then compare them.

Final Answer:
The vendor makes approximately a 77.7% profit on the bananas.