A vendor buys chikoos at the rate of 15 for Rs. 8 and sells them at the rate of 10 for Rs. 6. Based on this buying and selling scheme, what is his percentage gain or loss on the cost price?

Introduction / Context:
In this question, the vendor purchases and sells chikoos in two different quantity-price combinations, namely “15 for Rs. 8” and “10 for Rs. 6”. These kinds of problems are common in profit and loss sections of quantitative aptitude because they require candidates to compute unit cost price and unit selling price and then compare them. The challenge lies in carefully handling the fractions and correctly determining whether the vendor makes a gain or a loss, and by what percentage relative to cost price.

Given Data / Assumptions:
- Purchase rate: 15 chikoos for Rs. 8. - Selling rate: 10 chikoos for Rs. 6. - All chikoos are identical; there is no wastage. - We must find the percentage profit or loss on the cost price.

Concept / Approach:
The essential steps are to compute the cost price (CP) per chikoo and the selling price (SP) per chikoo. Cost price per chikoo is total cost divided by the number purchased in that batch; selling price per chikoo is total selling amount divided by the number sold in that batch. Once CP and SP per unit are known, profit per chikoo = SP - CP. The profit percentage is then Profit% = (Profit / CP) * 100. If SP is greater than CP, there is a gain; if SP is lower than CP, there is a loss. Working with per-unit values makes the logic transparent and avoids confusion about how many chikoos are involved.

Step-by-Step Solution:
Purchase rate: 15 chikoos for Rs. 8. Cost price per chikoo = 8 / 15 rupees. Selling rate: 10 chikoos for Rs. 6. Selling price per chikoo = 6 / 10 = 3 / 5 rupees = 0.6 rupees. Now compare CP and SP in fraction form. CP per chikoo = 8 / 15 ≈ 0.5333 rupees. SP per chikoo = 3 / 5 = 0.6 rupees. Profit per chikoo = SP - CP = (3 / 5) - (8 / 15). Compute: (3 / 5) - (8 / 15) = (9 / 15) - (8 / 15) = 1 / 15 rupee. Profit percentage = (Profit / CP) * 100 = (1 / 15) / (8 / 15) * 100. Simplify: (1 / 15) * (15 / 8) * 100 = (1 / 8) * 100 = 12.5%. Therefore, the vendor gains 12.5%.

Verification / Alternative check:
Take a common multiple of 15 and 10, such as 30 chikoos. Cost for 30 chikoos: he buys 15 for Rs. 8, so 30 for Rs. 16. Selling for 30 chikoos: he sells 10 for Rs. 6, so 30 for Rs. 18. Profit on 30 chikoos = 18 - 16 = Rs. 2. Profit% = 2 / 16 * 100 = 12.5%, which matches the earlier calculation.

Why Other Options Are Wrong:
- 12.5 percent loss is incorrect because SP > CP here, so there is clearly a gain. - 11.11 percent gain or 11.1 percent loss come from mixing up the ratios or using 9-for-10 style approximations. - 10 percent gain is an underestimation that does not match the precise fractional calculation.

Common Pitfalls:
Some students directly compare 15 and 10 or 8 and 6 without converting to per-unit prices, which leads to wrong conclusions. Another frequent mistake is to calculate profit percentage on the selling price instead of on the cost price. Rounding off decimal approximations too early, instead of working with exact fractions, can cause slight but important errors in the final percentage.

Final Answer:
The vendor makes a 12.5 percent gain on the cost price.