A man gains 15% by selling a calculator at a certain price. If he sells the same calculator at three times that price, what will be his profit percentage?

Introduction / Context:
This question explores how profit percentage changes when the selling price is scaled by a factor while cost price remains the same. Initially, the man sells a calculator at a price that yields a 15% gain. Then he sells at three times that price. Because profit percentage depends on the difference between selling price and cost price relative to cost price, multiplying the selling price changes the profit dramatically. This is a good test of algebraic reasoning with percentages.

Given Data / Assumptions:
- At the original selling price, the man gains 15%. - Let the original selling price be P. - The new selling price is 3P. - Cost price of the calculator remains unchanged. - We need to find the new profit percentage when selling at 3P.

Concept / Approach:
Let the cost price be C. A 15% profit at selling price P means P = 1.15 * C. The new selling price is 3P = 3 * 1.15 * C = 3.45 * C. Profit in the new case is 3.45 * C - C = 2.45 * C. Profit percentage is (Profit / C) * 100 = 2.45 * 100 = 245%. This applies the basic formula for profit percentage but uses the earlier relationship between selling price and cost price to express everything in terms of C.

Step-by-Step Solution:
Step 1: Let cost price of the calculator be C. Step 2: At the original selling price P, profit is 15% of C. Step 3: Therefore, P = C * 1.15. Step 4: New selling price is 3P = 3 * 1.15 * C. Step 5: So new selling price = 3.45 * C. Step 6: New profit = New SP - CP = 3.45 * C - C. Step 7: New profit = 2.45 * C. Step 8: New profit percentage = (New profit / CP) * 100. Step 9: New profit percentage = (2.45 * C / C) * 100 = 2.45 * 100. Step 10: New profit percentage = 245%.

Verification / Alternative check:
Take an easy cost price for a quick check. Let C = Rs. 100. Then 15% profit gives SP P = Rs. 115. The new selling price is 3 * 115 = Rs. 345. Profit in this case is 345 - 100 = Rs. 245. Profit percentage = 245 / 100 * 100 = 245%. This numerical example confirms the algebraic result that profit percentage becomes 245% when selling at three times the original selling price that gave a 15% profit.

Why Other Options Are Wrong:
125% and 175% are too low and would correspond to much smaller increases in selling price above cost. For example, a 125% profit would mean selling at 2.25 times cost price, which is less than 3.45 times cost price in this problem. 225% profit still does not match the actual calculation. Only 245% fits the relationship derived from the original 15% gain and the threefold increase in selling price.

Common Pitfalls:
A frequent mistake is to simply triple the 15% profit and assume 45% as the new profit percentage, which is incorrect because the base (selling price relative to cost price) changes. Another pitfall is to think that the new profit percentage is calculated on the original selling price instead of cost price. Always work through an algebraic expression using cost price as the base to avoid these conceptual errors.

Final Answer:
When the calculator is sold at three times the original selling price, the man's profit percentage becomes 245%.