A vendor buys bananas at the rate of 9 for Rs 8 and sells them at the rate of 8 for Rs 9. What is his profit or loss percentage?

Introduction / Context:
This is another unit rate profit and loss question, similar to the oranges problem. Instead of giving direct per unit prices, the vendor's buying and selling prices are described in terms of groups of bananas. The task is to compute cost price per banana and selling price per banana and then determine the percentage profit or loss.

Given Data / Assumptions:

• The vendor buys 9 bananas for Rs 8.
• He sells 8 bananas for Rs 9.
• We must find the profit or loss percentage.
• All bananas bought are sold and there is no wastage.

Concept / Approach:
First we find cost per banana: CP per banana = total cost divided by number of bananas purchased. Then we find selling price per banana: SP per banana = total selling price divided by number of bananas sold. Using these, we compute Profit% = (SP - CP) / CP * 100. Since one group relates 9 bananas to Rs 8 and the other relates 8 bananas to Rs 9, converting to per piece rates is essential.

Step-by-Step Solution:
Buying rate: 9 bananas cost Rs 8, so CP per banana = 8 / 9 rupees.Selling rate: 8 bananas sell for Rs 9, so SP per banana = 9 / 8 rupees.CP per banana = 8 / 9 ≈ 0.8889.SP per banana = 9 / 8 = 1.125.Profit per banana = SP - CP = 1.125 - 0.8889 ≈ 0.2361.Profit percentage = (profit per banana / CP per banana) * 100 ≈ (0.2361 / 0.8889) * 100.0.2361 / 0.8889 ≈ 0.265625, so profit percentage ≈ 26.5625%.Rounded suitably, this is 26.56% profit.

Verification / Alternative check:
Take a common multiple of the quantities to avoid decimals. For example, buy 72 bananas. At 9 for Rs 8, number of groups is 72 / 9 = 8, so cost = 8 * 8 = Rs 64. Sell 72 bananas at 8 for Rs 9, groups = 72 / 8 = 9, total revenue = 9 * 9 = Rs 81. Profit = 81 - 64 = Rs 17. Profit percentage = 17 / 64 * 100 ≈ 26.5625%, confirming the earlier calculation.

Why Other Options Are Wrong:
13.28% profit or loss values correspond to roughly half the correct percentage and result from miscalculations or using inverse ratios. 26.56% loss is impossible here because SP per banana is larger than CP per banana. Only 26.56% profit matches the numbers derived from consistent per unit comparisons.

Common Pitfalls:
Some learners invert one of the fraction rates or compare 9 for 8 and 8 for 9 directly without converting to per banana figures. This can lead to wrong conclusions about whether there is profit or loss. Always reduce such grouped rate problems to per unit prices and then apply the profit formula systematically.

Final Answer:
The vendor makes a 26.56% profit on selling the bananas.