By selling an article for Rs. 800, a shopkeeper makes a profit of 25% on its cost price. At what price should he sell the same article in order to incur a loss of 25% on the cost price?

Introduction / Context:
This question is a straightforward application of profit and loss percentage on the same cost price. First, the shopkeeper sells the article at a profit. We use that information to determine the cost price. Then we are asked to find the selling price that would result in a specific loss percentage on that same cost price. This is common in exam questions that check basic understanding of percentage changes applied to cost price.

Given Data / Assumptions:

• Selling price with profit = Rs. 800.
• Profit at this price = 25% of cost price.
• We assume a single fixed cost price for the article.
• Required: selling price that gives a 25% loss on the same cost price.
• All transactions are independent but based on the same cost price.

Concept / Approach:
If profit is 25% of cost price, then selling price equals 125% of cost price. Using SP = 1.25 * CP and the given selling price, we find CP. For the required situation, a 25% loss means selling price should be 75% of cost price. Thus we multiply the cost price by 0.75. Working entirely in terms of cost price ensures the calculation is systematic and avoids mistakes with direct proportionality on selling price.

Step-by-Step Solution:
Step 1: Let cost price = CP. Step 2: Given that a 25% profit gives SP = Rs. 800, so 800 = CP * (1 + 25/100) = CP * 1.25. Step 3: Therefore, CP = 800 / 1.25. Step 4: Compute CP: 800 / 1.25 = 800 * (4/5) = 640. Step 5: To get a 25% loss, SP must be 75% of CP, i.e., SP = 0.75 * CP. Step 6: Required SP = 0.75 * 640 = 480. Step 7: Hence, the article must be sold for Rs. 480 to incur a 25% loss.

Verification / Alternative check:
Check both scenarios explicitly. With CP = Rs. 640 and SP = Rs. 800, profit = 800 - 640 = Rs. 160, profit percentage = (160 / 640) * 100 = 25%. With SP = Rs. 480, loss = 640 - 480 = Rs. 160, loss percentage = (160 / 640) * 100 = 25%. The symmetry in gain and loss confirms that the calculations are correct.

Why Other Options Are Wrong:
Selling the article for Rs. 720 or Rs. 640 would still give a profit or no loss on a cost price of Rs. 640. A price of Rs. 540 would generate a smaller loss percentage, not exactly 25%, while Rs. 600 would give only a modest loss or even very small loss relative to CP. Only Rs. 480 yields a 25% loss.

Common Pitfalls:
A frequent error is to treat the given selling price of Rs. 800 as 125% of Rs. 800, or to decrease that directly by 25% instead of first computing the cost price. Another mistake is to apply 25% loss to the selling price rather than the cost price. Always remember that both profit and loss percentages are applied on the cost price unless stated otherwise.

Final Answer:
The shopkeeper should sell the article for Rs. 480 to incur a 25% loss on the cost price.