By selling an article for Rs1,008. A suffers as much loss as she would have gained by selling it at a 20% profit. If she sells it for Rs 1,354.50, then her profit percentage is:

Options

A. `8%`
B. `10%`
C. `12.5%`
D. `7.5%`

Answer

To solve the problem step by step, we need to find the cost price (CP) of the article first and then calculate the profit percentage when sold for Rs 1,354.50.

### Step 1: Understand the relationship between selling price (SP) and cost price (CP)
The question states that selling the article for Rs 1,008 results in a loss equal to the profit that would have been made if it was sold at a 20% profit.

### Step 2: Set up the equations
Let the cost price of the article be \( CP \).

- Selling Price at a 20% profit:
\[ SP_{20\%} = CP + 0.2 \times CP = 1.2 \times CP \]

- Loss when sold for Rs 1,008:
\[ Loss = CP - 1008 \]

According to the problem, the loss when sold for Rs 1,008 is equal to the profit that would have been made at a 20% profit:
\[ CP - 1008 = 1.2 \times CP - CP \]
\[ CP - 1008 = 0.2 \times CP \]

### Step 3: Rearranging the equation
Rearranging the equation gives:
\[ CP - 0.2 \times CP = 1008 \]
\[ 0.8 \times CP = 1008 \]

### Step 4: Solve for CP
Now, we can solve for \( CP \):
\[ CP = \frac{1008}{0.8} = 1260 \]

### Step 5: Calculate the profit when sold for Rs 1,354.50
Now that we have the cost price, we can find the profit when the article is sold for Rs 1,354.50:
\[ Profit = Selling Price - Cost Price = 1354.50 - 1260 = 94.50 \]

### Step 6: Calculate the profit percentage
Finally, we can calculate the profit percentage:
\[ Profit \% = \left( \frac{Profit}{CP} \right) \times 100 = \left( \frac{94.50}{1260} \right) \times 100 \]
\[ Profit \% = 7.5\% \]

### Final Answer
The profit percentage when the article is sold for Rs 1,354.50 is **7.5%**.