A vendor buys oranges at the rate of 5 for Rs 6 and sells them at the rate of 2 for Rs 3. What is his overall result on this trade in percentage terms (profit or loss)?

Introduction / Context:
This is a classic cost per unit and selling price per unit type profit and loss question. The vendor changes the quantity in which he buys and sells, and the price per piece changes accordingly. The main test here is whether you can correctly compute cost price per orange and selling price per orange, and then decide the percentage profit or loss.

Given Data / Assumptions:

• The vendor buys 5 oranges for Rs 6.
• He sells oranges at 2 for Rs 3.
• We need to determine the profit or loss percentage.
• We assume there is no wastage or spoilage and that all bought oranges are sold.

Concept / Approach:
The key idea is to find price per orange in both buying and selling. Cost price per orange is total cost divided by number of oranges purchased. Selling price per orange is total selling price divided by number of oranges sold. Then standard percentage formula is used: Profit% = (SP - CP) / CP * 100. If the result is positive, it is profit, otherwise it is loss.

Step-by-Step Solution:
Buying rate: 5 oranges cost Rs 6, so cost price per orange = 6 / 5 = Rs 1.20.Selling rate: 2 oranges sold for Rs 3, so selling price per orange = 3 / 2 = Rs 1.50.Profit per orange = SP - CP = 1.50 - 1.20 = Rs 0.30.Profit percentage = (profit per orange / cost price per orange) * 100.Profit percentage = (0.30 / 1.20) * 100 = 0.25 * 100 = 25%.Therefore, the vendor makes a 25 percent gain.

Verification / Alternative check:
Consider buying 10 oranges. At the buying rate, 10 oranges cost 2 * Rs 6 = Rs 12. Selling 10 oranges at 2 for Rs 3 means 5 groups of 2, each group yielding Rs 3, so total SP = 5 * 3 = Rs 15. Profit = 15 - 12 = Rs 3, and profit percentage = 3 / 12 * 100 = 25%, confirming our earlier calculation.

Why Other Options Are Wrong:
20 percent gain would correspond to a smaller difference between SP and CP per orange. 25 percent loss or 20 percent loss would require selling price to be less than cost price, which is not the case here since 1.50 is clearly more than 1.20. Therefore all options showing loss or 20 percent gain are inconsistent with the actual numbers.

Common Pitfalls:
A common misunderstanding is to compare 5 for 6 and 2 for 3 directly without converting to per unit rates. Some students also mistake 5 and 2 as directly comparable quantities and miscompute ratios. Always reduce such problems to a per item cost and per item selling price to avoid confusion and calculation errors.

Final Answer:
The vendor makes a 25 percent gain on selling the oranges.