If the selling price of an article is doubled and as a result the profit becomes three times the original profit, what is the original profit percentage on the article?

Introduction / Context:
This is an algebra-based profit and loss problem that focuses on understanding the relationship between selling price and profit. The problem states that when the selling price is doubled, the profit becomes three times the original profit. From this, we are asked to deduce the original profit percentage. It is a standard conceptual question used to test the ability to create and solve simple equations using profit definitions.

Given Data / Assumptions:

• Original cost price of the article = C.
• Original selling price of the article = S.
• Original profit = S − C.
• New selling price = 2S.
• New profit = 2S − C.
• New profit is three times original profit: 2S − C = 3(S − C).

Concept / Approach:
Profit is defined as selling price minus cost price. The relationship between original and new profits is given directly. We set up an equation using this relationship and solve for the ratio S:C. Once the ratio S:C is known, we can compute the profit as a fraction of cost price and then convert it into a percentage. This is a pure algebraic reasoning question with no actual numerical values required.

Step-by-Step Solution:
Let cost price = C and original selling price = S.Original profit = P = S − C.New selling price = 2S.New profit = 2S − C.We are told that new profit is three times original profit: 2S − C = 3(S − C).Expand the right side: 2S − C = 3S − 3C.Bring all terms to one side: 2S − C − 3S + 3C = 0.Simplify: −S + 2C = 0 ⇒ S = 2C.Original profit P = S − C = 2C − C = C.Profit percentage = (P / C) * 100 = (C / C) * 100 = 100%.

Verification / Alternative check:
Take a convenient example: let C = Rs. 100.Then S = 2C = Rs. 200 based on S = 2C.Original profit = 200 − 100 = Rs. 100, which is 100% of the cost price.New selling price = 2S = Rs. 400.New profit = 400 − 100 = Rs. 300.This is exactly three times the original profit (3 * 100 = 300), so the condition is satisfied.

Why Other Options Are Wrong:
66.6%, 150%, and 190% do not satisfy the equation 2S − C = 3(S − C) when you derive S in terms of C.Only when profit equals 100% of cost price (that is, S = 2C) do we get a tripling of profit after doubling the selling price.

Common Pitfalls:
One common mistake is to guess that doubling selling price doubles profit, which is not necessarily true.Another is to assume fixed rupee increases instead of working symbolically with C and S.Students may also incorrectly set up the equation, for example, writing 2S − C = 3S instead of relating it to S − C.

Final Answer:
The original profit percentage on the article is 100% of its cost price.