A sells a article to B at a profit of 10% B sells the article back to A at a loss of 10%. In this transaction

Options

A. A neither loses nor gains
B. A makes a profit of 11%
C. A makes a profit of 20%
D. В loses 20%

Answer

To solve the problem step by step, we will analyze the transactions between A and B, starting with the cost price of the article.

### Step 1: Define the Cost Price
Let the cost price (CP) of the article for A be \(100\) rupees.

### Step 2: Calculate Selling Price from A to B
A sells the article to B at a profit of \(10\%\).
- Profit = \(10\%\) of \(100 = 10\) rupees.
- Therefore, the selling price (SP) from A to B = CP + Profit = \(100 + 10 = 110\) rupees.

### Step 3: Calculate Selling Price from B to A
B sells the article back to A at a loss of \(10\%\).
- Loss = \(10\%\) of \(110 = 11\) rupees.
- Therefore, the selling price (SP) from B to A = CP - Loss = \(110 - 11 = 99\) rupees.

### Step 4: Calculate Profit or Loss for A
Now we need to determine the profit or loss for A in this entire transaction.
- A's initial cost price was \(100\) rupees.
- A sold the article to B for \(110\) rupees and bought it back from B for \(99\) rupees.
- Profit for A = Selling Price from A to B - Cost Price from B to A = \(110 - 99 = 11\) rupees.

### Step 5: Calculate Profit Percentage for A
To find the profit percentage for A:
- Profit Percentage = \(\frac{\text{Profit}}{\text{Cost Price}} \times 100\)
- Profit Percentage = \(\frac{11}{100} \times 100 = 11\%\)

### Conclusion
A makes a profit of \(11\%\) in this transaction.

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