Two shopkeepers sell the same article for the same selling price. The first shopkeeper calculates his profit percentage on the selling price, and the second shopkeeper calculates his profit percentage on the cost price. For both of them the profit percentage is stated as 25 percent. If the difference between their rupee profits is Rs. 175, what is the sum of the cost prices for both shopkeepers together?

Introduction / Context:
This problem highlights an important conceptual difference between profit calculated on selling price and profit calculated on cost price. Even though the numerical percentage is the same, using a different base produces different rupee profits. The question links these two profit amounts through a common selling price and a known difference in rupee profit, and asks for the combined cost prices of both shopkeepers.

Given Data / Assumptions:

• Both shopkeepers sell the article at the same selling price S.
• First shopkeeper calculates profit as 25 percent of the selling price.
• Second shopkeeper calculates profit as 25 percent of the cost price.
• The difference between their profits is Rs. 175.
• We must find the sum of their cost prices.

Concept / Approach:
Let the common selling price be S. For the first shopkeeper, profit one equals 25 percent of S, so profit one equals 0.25 * S and his cost price is S minus profit one. For the second shopkeeper, profit two equals 25 percent of his own cost price C2, and selling price S equals C2 plus profit two. Using these relationships, we first express both profits in terms of S, then use the given difference of 175 rupees to find S. After that, we compute each cost price and add them together.

Step-by-Step Solution:
Let selling price for both be S rupees.First shopkeeper profit P1 equals 25 percent of S, so P1 equals 0.25 * S.His cost price C1 equals S minus P1 equals S minus 0.25 * S equals 0.75 * S.Second shopkeeper profit P2 equals 25 percent of his cost price C2, so P2 equals 0.25 * C2.His selling price S equals C2 plus P2 equals C2 + 0.25 * C2 equals 1.25 * C2, so C2 equals S / 1.25 equals 0.80 * S.Then P2 equals 0.25 * 0.80 * S equals 0.20 * S.The difference between their profits is P1 minus P2 equals 0.25 * S minus 0.20 * S equals 0.05 * S.We are given that this difference is 175 rupees, so 0.05 * S equals 175 and S equals 175 / 0.05 equals 3500 rupees.Now C1 equals 0.75 * 3500 equals 2625 rupees, and C2 equals 0.80 * 3500 equals 2800 rupees.Sum of cost prices equals 2625 plus 2800 which is 5425 rupees.

Verification / Alternative check:
We can verify by computing individual profits using S equals 3500 rupees. First shopkeeper profit is 25 percent of 3500 which is 875 rupees. Second shopkeeper cost price is 2800 rupees, so his profit is 25 percent of 2800 which is 700 rupees. The difference between these profits is 875 minus 700 equals 175 rupees, which matches the problem condition. This confirms that S and the calculated cost prices are consistent with all the given information.

Why Other Options Are Wrong:
Any other sum of cost prices would result from taking an incorrect selling price S or misapplying the percentage definitions. For example, if we incorrectly treated both percentages as based on cost price, the profit difference would not match 175 rupees. Similarly, sums like 4875, 4675, or 5275 do not arise from any consistent computation using the given percentages and the same selling price condition. Only 5425 rupees fits the derived equations.

Common Pitfalls:
One common mistake is to assume that both shopkeepers calculate profit on cost price, which makes the problem trivial and ignores the main concept being tested. Another error is mixing up which variable is the base for each percentage, leading to incorrect equations. Finally, some learners forget that the selling price for both shopkeepers is the same, which is crucial for linking their cost prices. Carefully distinguishing between profit on selling price and profit on cost price is essential here.

Final Answer:
The sum of the cost prices of the two shopkeepers is Rs. 5425.