A fruit vendor sells apples at Rs. 170 per kilogram and suffers a loss of 15% at this selling price. If instead he sells the apples at Rs. 230 per kilogram, what is his percentage profit on the cost price?

Introduction / Context:
This question tests basic understanding of profit and loss percentages when the selling price changes but the cost price per kilogram remains the same. The vendor initially sells at a loss, then raises the selling price and moves into profit. Many real-life pricing decisions by shopkeepers work in exactly this way, so mastering the underlying calculations is useful both for exams and daily life. The key is to correctly compute the cost price from the first scenario and then use that cost price in the second scenario to find the new profit percentage.

Given Data / Assumptions:
- Initial selling price (SP1) of apples = Rs. 170 per kg. - At SP1, the vendor suffers a loss of 15%. - New selling price (SP2) of apples = Rs. 230 per kg. - Cost price per kilogram is constant in both cases. - We must find the profit percentage at the new selling price.

Concept / Approach:
Under a loss of L%, the relationship between selling price and cost price is SP = CP * (1 - L/100). Using this, we can compute CP from SP1 and the 15% loss. Once CP is known, the new profit percentage when selling at SP2 is given by Profit% = ((SP2 - CP) / CP) * 100. It is crucial to always consider cost price as the base for both profit and loss calculations. Working systematically with these formulas prevents confusion between the two selling prices and their different profit or loss situations.

Step-by-Step Solution:
Given loss% = 15%, so SP1 = CP * (1 - 0.15) = CP * 0.85. Thus CP = SP1 / 0.85 = 170 / 0.85. Compute CP: CP = Rs. 200 per kg. Now, with SP2 = Rs. 230 per kg, profit per kg = SP2 - CP = 230 - 200. Profit per kg = Rs. 30. Profit percentage = (Profit / CP) * 100 = (30 / 200) * 100. Profit% = 0.15 * 100 = 15%.

Verification / Alternative check:
Check the loss in the first case: 15% of CP = 0.15 * 200 = Rs. 30, so SP1 = 200 - 30 = Rs. 170, which matches the given selling price. Check the profit in the second case: 15% of CP = Rs. 30, so SP2 should be 200 + 30 = Rs. 230, which confirms the calculation. Both checks align perfectly with the data, so the profit percentage of 15% is correct.

Why Other Options Are Wrong:
- 10% and 5%: These underestimate the profit and do not match the difference between CP and SP2. - 20%: This would give a profit of Rs. 40 per kg, leading to SP2 = Rs. 240, not Rs. 230. - 12%: This would make the selling price 200 * 1.12 = 224, again inconsistent with the given Rs. 230.

Common Pitfalls:
A common error is to mistakenly compute the loss or profit based on selling price instead of cost price. Some students incorrectly assume that changing from a 15% loss to a certain selling price automatically implies a symmetric 15% profit without checking the actual numbers. Another pitfall is to forget to first compute the cost price from the initial loss situation, which is essential to correctly answering the question.

Final Answer:
When sold at Rs. 230 per kilogram, the vendor earns a profit of 15%.