One trader calculates the percentage of profit on the buying price and another calculates on the selling price. When their selling prices are the same, then the difference of their actual profits is Rs. 85 and both claim to have made 20% profit. What is the selling price of each ?

Options

A. Rs. 1700
B. Rs. 2100
C. Rs. 2550
D. Rs. 2750

Answer

To solve the problem step by step, we will denote the selling price of both traders as SP.

### Step 1: Understand the profit calculations
- Trader 1 calculates profit based on the buying price (CP1).
- Trader 2 calculates profit based on the selling price (SP).

Both traders claim to have made a profit of 20%.

### Step 2: Express the selling prices in terms of cost prices
- For Trader 1, if the profit is 20%, then:
\[ SP = CP1 + 0.2 \times CP1 = 1.2 \times CP1 \]
Therefore, we can express CP1 as:
\[ CP1 = \frac{SP}{1.2} \]

- For Trader 2, if the profit is 20% based on the selling price, then:
\[ CP2 = SP - 0.2 \times SP = 0.8 \times SP \]

### Step 3: Set up the equation for the difference in profits
According to the problem, the difference in their actual profits is Rs. 85. The actual profit for each trader can be expressed as follows:
- Profit for Trader 1:
\[ Profit1 = SP - CP1 = SP - \frac{SP}{1.2} = SP \left(1 - \frac{1}{1.2}\right) = SP \left(\frac{0.2}{1.2}\right) = \frac{SP}{6} \]

- Profit for Trader 2:
\[ Profit2 = SP - CP2 = SP - 0.8 \times SP = 0.2 \times SP \]

### Step 4: Set up the equation for the difference in profits
The difference in profits is given as Rs. 85:
\[ Profit2 - Profit1 = 85 \]
Substituting the expressions for the profits:
\[ 0.2 \times SP - \frac{SP}{6} = 85 \]

### Step 5: Solve for SP
To solve the equation, first find a common denominator:
\[ \frac{6 \times 0.2 \times SP - SP}{6} = 85 \]
This simplifies to:
\[ \frac{1.2 \times SP - SP}{6} = 85 \]
\[ \frac{0.2 \times SP}{6} = 85 \]
Multiplying both sides by 6:
\[ 0.2 \times SP = 510 \]
Now, divide by 0.2:
\[ SP = \frac{510}{0.2} = 2550 \]

### Conclusion
The selling price of each trader is Rs. 2550.