One shopkeeper calculates his profit at C.P. and second at S.P. both gains profit of 20%. If S.P. of both is same and differences of both the profit is Rs 85 then find the S.P. ?

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Profit Calculation
The first shopkeeper calculates profit based on Cost Price (C.P.), while the second shopkeeper calculates profit based on Selling Price (S.P.). Both have a profit of 20%.

### Step 2: Calculate Selling Price for the First Shopkeeper
If we assume the Cost Price (C.P.) of the first shopkeeper is Rs 100, then:
- Profit = 20% of C.P. = 20% of 100 = Rs 20
- Selling Price (S.P.) = C.P. + Profit = 100 + 20 = Rs 120

### Step 3: Calculate Cost Price for the Second Shopkeeper
The second shopkeeper also has a profit of 20%, but this time it is based on Selling Price (S.P.). Let's denote the Selling Price of the second shopkeeper as Rs 120 (since both S.P.s are the same).
- Profit = 20% of S.P. = 20% of 120 = Rs 24
- Therefore, Cost Price (C.P.) = S.P. - Profit = 120 - 24 = Rs 96

### Step 4: Calculate the Profits of Both Shopkeepers
- Profit of the first shopkeeper = Rs 20 (from C.P. of Rs 100)
- Profit of the second shopkeeper = Rs 24 (from S.P. of Rs 120)

### Step 5: Find the Difference in Profits
The difference in profits between the two shopkeepers is:
- Difference = Profit of second shopkeeper - Profit of first shopkeeper = 24 - 20 = Rs 4

### Step 6: Set Up the Equation Based on Given Information
We know that the difference in profits is Rs 85. Therefore, we can set up the equation:
- 4 units (difference in profits) = Rs 85
- 1 unit = 85 / 4 = Rs 21.25

### Step 7: Calculate the Selling Price
Now we need to find the Selling Price (S.P.) based on the first shopkeeper's selling price:
- S.P. of first shopkeeper = 120 units
- S.P. = 120 * (85 / 4) = 120 * 21.25 = Rs 2550

### Conclusion
The Selling Price (S.P.) of both shopkeepers is Rs 2550.

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