A trader sells an article at a profit of 20% on its cost price. Had he bought that article at a price 60% lower than its original cost price and sold it for Rs. 90 less than the original selling price, he would have gained 50%. What is the original cost price of the article in rupees?

Introduction / Context:
This is a slightly tricky profit and loss problem where both the cost price and selling price are changed in a hypothetical scenario. Originally, the trader earns a 20% profit. In a second scenario, he imagines buying the article cheaper (60% less cost) and selling it for Rs. 90 less than the original selling price, resulting in a 50% profit. Using these conditions, we must determine the original cost price of the article.

Given Data / Assumptions:

• Let the original cost price (CP) be x rupees.
• Original profit percentage = 20%.
• Original selling price SP1 = 1.20x.
• In the hypothetical scenario, cost price CP2 = x − 60% of x = 0.40x.
• New selling price SP2 = SP1 − 90 = 1.20x − 90.
• In this scenario, profit percentage = 50%, so SP2 = 1.50 * CP2.

Concept / Approach:
We form an equation by equating the new selling price from the narrative description (1.20x − 90) to the selling price expression derived from the 50% profit condition (1.5 * 0.40x). This gives a simple linear equation in x. Solving that equation yields the original cost price. This method ensures both scenarios are correctly captured in one mathematical relationship.

Step-by-Step Solution:
Let the original cost price be x rupees. Original selling price SP1 = 1.20x (because profit is 20%). In the second scenario, new cost price CP2 = 40% of x = 0.40x. New selling price SP2 is Rs. 90 less than SP1, so SP2 = 1.20x − 90. This SP2 gives a profit of 50% on CP2, so SP2 = 1.50 * CP2. Therefore, 1.20x − 90 = 1.50 * 0.40x. Compute the right-hand side: 1.50 * 0.40x = 0.60x. So the equation becomes: 1.20x − 90 = 0.60x. Rearrange: 1.20x − 0.60x = 90. 0.60x = 90. x = 90 / 0.60 = 150. Thus, the original cost price of the article is Rs. 150.

Verification / Alternative check:
With CP = 150, original SP1 = 1.20 * 150 = Rs. 180. In the second scenario, CP2 = 40% of 150 = Rs. 60. SP2 calculated from the condition is SP1 − 90 = 180 − 90 = Rs. 90. Profit in the second scenario = 90 − 60 = Rs. 30. Profit percentage = (30 / 60) * 100 = 50%, which matches the problem statement. Therefore, CP = Rs. 150 is consistent with both scenarios.

Why Other Options Are Wrong:
200, 250, 300 and 180: Substituting any of these values for x fails to satisfy the relationship 1.20x − 90 = 0.60x, and the 50% profit condition breaks. For example, if x = 200, then SP1 = 240 and SP2 = 150, while CP2 = 80. Profit = 70, which is not 50% of 80.

Common Pitfalls:
Students sometimes confuse “bought at 60% less price” with “bought at 60% of the original price,” which is wrong. The phrase “60% less” means 40% of the original price, not 60%. Another error is to ignore the requirement that SP2 has to be Rs. 90 less than SP1 and instead relate SP2 directly to CP without using the original selling price. Writing the equations clearly from the wording helps avoid misinterpretation.

Final Answer:
The original cost price of the article is Rs. 150.