If the selling price of an article is doubled, the trader's profit becomes three times the original profit. What is the original profit percentage on the article?

Introduction / Context:
This is an algebraic profit–loss question involving relationships between cost price, selling price, and profit. You are told how the profit changes when the selling price is doubled, and you must deduce the original profit percentage. This requires careful algebraic setup using variables for cost price and selling price.

Given Data / Assumptions:
- Let original cost price (CP) of the article be C rupees.
- Let original selling price (SP) of the article be S rupees.
- Original profit = S - C.
- When the selling price is doubled, the new selling price is 2S.
- New profit becomes three times the original profit.

Concept / Approach:
The key step is to convert the statement "If selling price is doubled, the profit triples" into an equation. Original profit is S - C. New profit is 2S - C. According to the question, 2S - C = 3(S - C). Solving this equation gives a relationship between S and C, which we then convert into a profit percentage: profit percent = ((S - C) / C) * 100.

Step-by-Step Solution:
Step 1: Original profit = S - C.Step 2: After doubling the selling price, new SP = 2S, so new profit = 2S - C.Step 3: Given that the new profit is three times the original profit, we have 2S - C = 3(S - C).Step 4: Expand the right side: 2S - C = 3S - 3C.Step 5: Rearrange terms: bring all to one side: 2S - C - 3S + 3C = 0.Step 6: Simplify: (2S - 3S) + (-C + 3C) = -S + 2C = 0.Step 7: Hence -S + 2C = 0 which gives S = 2C.Step 8: Original profit = S - C = 2C - C = C.Step 9: Profit percentage = (profit / cost price) * 100 = (C / C) * 100 = 100%.

Verification / Alternative check:
Take a simple numerical example. Let C = Rs. 100. Then S = 2C = Rs. 200. Original profit = 200 - 100 = Rs. 100, which is 100% of cost. After doubling SP, new SP = 2S = Rs. 400. New profit = 400 - 100 = Rs. 300. New profit is exactly three times the original profit (3 * 100 = 300), confirming the algebraic solution and the 100% profit rate.

Why Other Options Are Wrong:
200%, 300%, or 400% profit would imply far larger original profits than the condition allows when you double the selling price. For example, if original profit were 200%, then S would be 3C, and doubling S would not lead to only triple profit. 50% profit similarly fails to satisfy the 2S - C = 3(S - C) condition. Only 100% matches the equation derived from the problem.

Common Pitfalls:
Many students misinterpret the phrase "profit triples" as "profit increases by 300%" or confuse it with tripling of the selling price. Others substitute arbitrary values without setting up a general equation, leading to inconsistent results. Keeping track of cost price, selling price, and profit with clear variables helps avoid these misunderstandings.

Final Answer:
The original profit percentage on the article is 100%.