There are two shopkeepers, first shopkeeper calculates his profit percent on the selling price whereas the second shopkeeper calculates his profit percent on the cost price. If the selling price for both the shopkeeper is same and the difference between their profits is ₹17 5. Then, calculate the sum of the cost price for both the shopkeeper if the profit percent for the both shopkeeper is 25%?

Options

A. ₹5425
B. ₹4875
C. ₹4675
D. ₹5275

Explanation

To solve the problem, we will follow a step-by-step approach:

### Step 1: Understand the Problem
We have two shopkeepers:
- Shopkeeper 1 calculates profit percentage on Selling Price (SP).
- Shopkeeper 2 calculates profit percentage on Cost Price (CP).
- Both have the same Selling Price, and the difference between their profits is ₹175.
- The profit percentage for both is 25%.

### Step 2: Define Variables
Let:
- SP = Selling Price (assumed to be ₹100 for simplicity)
- CP1 = Cost Price of Shopkeeper 1
- CP2 = Cost Price of Shopkeeper 2

### Step 3: Calculate Profit for Shopkeeper 1
For Shopkeeper 1:
- Profit = 25% of SP
- Profit = 25% of ₹100 = ₹25
- Therefore, CP1 = SP - Profit = ₹100 - ₹25 = ₹75

### Step 4: Calculate Profit for Shopkeeper 2
For Shopkeeper 2:
- Profit is calculated on CP, so:
- Let the CP2 be x.
- Selling Price = CP2 + Profit
- Profit = 25% of CP2 = 0.25 * CP2
- Therefore, SP = CP2 + 0.25 * CP2 = 1.25 * CP2
- Since SP = ₹100, we have:
\[ 1.25 * CP2 = 100 \implies CP2 = \frac{100}{1.25} = ₹80 \]

### Step 5: Calculate Profits
- Profit for Shopkeeper 1 = ₹25
- Profit for Shopkeeper 2 = 25% of CP2 = 25% of ₹80 = ₹20

### Step 6: Verify the Difference in Profits
- Difference in profits = Profit of Shopkeeper 1 - Profit of Shopkeeper 2
- Difference = ₹25 - ₹20 = ₹5
- However, we need to scale this to match the given difference of ₹175.
- Since the difference is ₹5, we can find the scaling factor:
\[ \text{Scaling Factor} = \frac{175}{5} = 35 \]

### Step 7: Calculate Actual Profits
- Actual Profit for Shopkeeper 1 = ₹25 * 35 = ₹875
- Actual Profit for Shopkeeper 2 = ₹20 * 35 = ₹700

### Step 8: Calculate Cost Prices
- Actual CP1 = ₹75 * 35 = ₹2625
- Actual CP2 = ₹80 * 35 = ₹2800

### Step 9: Calculate the Sum of Cost Prices
- Sum of Cost Prices = CP1 + CP2 = ₹2625 + ₹2800 = ₹5425

### Final Answer
The sum of the cost price for both shopkeepers is **₹5425**.

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