x and y are two articles sold by a trader. The cost price of x equals the selling price of y. x is sold at 25% profit, y's cost price is 25% less than it's selling price. Find the overall profit/loss percentage made by the trader.

Options

A. 0
B. `33(1)/(3)%`
C. `28(4)/(7)%`
D. 20

Answer

To solve the problem step by step, let's denote the following:

- Let the cost price of article X be \( CP_x \).
- Let the selling price of article Y be \( SP_y \).

### Step 1: Establish the relationship between \( CP_x \) and \( SP_y \)
According to the question, the cost price of X equals the selling price of Y:
\[ CP_x = SP_y \tag{1} \]

### Step 2: Calculate the selling price of article X
X is sold at a 25% profit. Therefore, the selling price of X can be calculated as:
\[ SP_x = CP_x + 0.25 \times CP_x = 1.25 \times CP_x = \frac{125}{100} \times CP_x = \frac{5}{4} CP_x \tag{2} \]

### Step 3: Establish the relationship for article Y's cost price
It is given that the cost price of Y is 25% less than its selling price. Therefore:
\[ CP_y = SP_y - 0.25 \times SP_y = 0.75 \times SP_y = \frac{75}{100} \times SP_y \tag{3} \]

### Step 4: Calculate total cost price
Now, we can express the total cost price (CP) of both articles:
\[ Total\ CP = CP_x + CP_y \]
Substituting equations (1) and (3) into this:
\[ Total\ CP = SP_y + \frac{75}{100} SP_y = SP_y + 0.75 SP_y = 1.75 SP_y \tag{4} \]

### Step 5: Calculate total selling price
Next, we calculate the total selling price (SP) of both articles:
\[ Total\ SP = SP_x + SP_y \]
Substituting equation (2) into this:
\[ Total\ SP = \frac{5}{4} CP_x + SP_y \]
From equation (1), we know \( CP_x = SP_y \):
\[ Total\ SP = \frac{5}{4} SP_y + SP_y = \frac{5}{4} SP_y + \frac{4}{4} SP_y = \frac{9}{4} SP_y \tag{5} \]

### Step 6: Calculate profit or loss percentage
Now, we can find the profit or loss percentage using the formula:
\[ Profit\ Percentage = \frac{Total\ SP - Total\ CP}{Total\ CP} \times 100 \]
Substituting equations (4) and (5):
\[ Profit\ Percentage = \frac{\frac{9}{4} SP_y - 1.75 SP_y}{1.75 SP_y} \times 100 \]
Converting \( 1.75 SP_y \) to a fraction:
\[ 1.75 SP_y = \frac{7}{4} SP_y \]
Now substituting:
\[ Profit\ Percentage = \frac{\frac{9}{4} SP_y - \frac{7}{4} SP_y}{\frac{7}{4} SP_y} \times 100 = \frac{\frac{2}{4} SP_y}{\frac{7}{4} SP_y} \times 100 \]
The \( SP_y \) cancels out:
\[ Profit\ Percentage = \frac{2}{7} \times 100 = \frac{200}{7} \approx 28.57\% \]

### Final Answer
The overall profit percentage made by the trader is approximately **28.57%**.

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