A shopkeeper sells an article at ₹ 40 and gets X% profit. However, when he sells it at ₹ 20, he faces same percentage of loss. What is the original cost of the article?

1. Analyze the context from PYQs: The 2014 exam taught us to be careful about the 'Base' in percentage problems [4]. Here, we have a single article, so the Cost Price (Base) is the same for both the profit and loss scenarios.\n2. We are given that the profit percentage and loss percentage are equal. Since they are calculated on the same Base (CP), the actual money value of the profit and loss must also be equal.\n3. This means the Cost Price is a value that is equidistant from the selling price of ₹40 and the selling price of ₹20.\n4. From the 2017 PYQ analysis, we know that a value lying exactly in the middle of two numbers is their 'Arithmetic Mean' or 'Balance Point' [11, 14].\n5. Calculation: Average of 40 and 20 = (40 + 20) / 2 = 60 / 2 = 30.\n6. Verification: If CP is 30, selling at 40 is a gain of 10. Selling at 20 is a loss of 10. Both represent a 33.33% change on the base of 30. The logic holds.