If the cost price of a certain article doubles, then the loss in rupees becomes three times what it was initially (selling price remains the same). What was the initial loss percentage on the cost price?

Introduction / Context:
This question examines the effect of changing cost price while keeping the selling price constant. The loss in rupees is said to become three times its original value when the cost price doubles. We must find what the original loss percentage was. This type of question checks conceptual understanding of how profit and loss amounts relate to cost price and selling price through basic algebraic relationships.

Given Data / Assumptions:

• Original cost price = C (unknown).
• Original selling price = S (unchanged later).
• Original loss = C - S (assuming C > S).
• New cost price after doubling = 2C.
• New loss = 2C - S.
• Given that new loss = 3 × original loss.
• We must find original loss percentage = (C - S) / C * 100.

Concept / Approach:
We set up an equation that the new loss equals three times the original loss: 2C - S = 3(C - S). This involves only C and S. Solving this equation gives a relationship between S and C. Once we know S in terms of C, we can substitute into the expression for loss percentage (C - S) / C * 100. Since C cancels in the ratio, we obtain a numeric percentage without needing actual values for C or S.

Step-by-Step Solution:
Step 1: Original loss = C - S. Step 2: New cost price = 2C, selling price is still S, so new loss = 2C - S. Step 3: Given that new loss is three times original loss: 2C - S = 3(C - S). Step 4: Expand right side: 3(C - S) = 3C - 3S. Step 5: Equation becomes 2C - S = 3C - 3S. Step 6: Rearrange: 2C - S - 3C + 3S = 0 → -C + 2S = 0. Step 7: So 2S = C, hence S = C/2. Step 8: Original loss = C - S = C - C/2 = C/2. Step 9: Loss percentage = (original loss / cost price) * 100 = (C/2) / C * 100 = (1/2) * 100 = 50%.

Verification / Alternative check:
Choose C = Rs. 100 for simplicity. Then S = C/2 = Rs. 50. Original loss = 100 - 50 = Rs. 50. New cost price = 200, selling price still 50, new loss = 200 - 50 = Rs. 150. Compare: new loss is 150, original loss was 50, and 150 = 3 × 50. Original loss percent = (50 / 100) * 100 = 50%, which matches our algebraic result.

Why Other Options Are Wrong:
Loss percentages of 25%, 75%, 40% or 0% do not give the exact threefold relationship when cost price is doubled and selling price is held constant. For example, with 25% loss, the algebraic relationship 2C - S = 3(C - S) would not hold. Only 50% loss creates the exact multiplication of the loss amount as described in the question.

Common Pitfalls:
A common error is to try to guess percentages without setting up the equation, or to incorrectly assume that doubling cost price doubles the loss percentage. Another mistake is mixing up the roles of cost and selling price when writing the loss expressions. Writing everything in terms of C and S and proceeding step by step avoids such confusion.

Final Answer:
The initial loss percentage on the article was 50 %.