When a person sells an article for Rs 1.200. he earns a profit that is equal to twice the amount of loss he would incur on selling the article for Rs 750. If he sells the article for Rs 925.20. then there is a:

Options

A. gain of `3%`
B. loss of `2.8%`
C. gain of `2.8%`
D. loss of `2.6%`

Answer

To solve the problem step by step, we will define the cost price (CP) and analyze the given information to find the profit or loss when the article is sold at different prices.

### Step 1: Define the Cost Price (CP)
Let the cost price of the article be \( CP = X \).

### Step 2: Calculate Profit when Selling for Rs 1200
When the article is sold for Rs 1200, the profit can be calculated as:
\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = 1200 - X \]

### Step 3: Calculate Loss when Selling for Rs 750
When the article is sold for Rs 750, the loss can be calculated as:
\[ \text{Loss} = \text{Cost Price} - \text{Selling Price} = X - 750 \]

### Step 4: Set Up the Equation Based on Given Condition
According to the problem, the profit when selling for Rs 1200 is equal to twice the loss incurred when selling for Rs 750:
\[ 1200 - X = 2(X - 750) \]

### Step 5: Simplify the Equation
Expanding the right side of the equation:
\[ 1200 - X = 2X - 1500 \]

### Step 6: Rearranging the Equation
Rearranging the equation gives:
\[ 1200 + 1500 = 2X + X \]
\[ 2700 = 3X \]

### Step 7: Solve for Cost Price (CP)
Dividing both sides by 3:
\[ X = \frac{2700}{3} = 900 \]
So, the cost price \( CP = 900 \).

### Step 8: Calculate Profit/Loss when Selling for Rs 925.20
Now, we need to find out the profit or loss when the article is sold for Rs 925.20:
\[ \text{Selling Price} = 925.20 \]
\[ \text{Profit or Loss} = \text{Selling Price} - \text{Cost Price} = 925.20 - 900 = 25.20 \]

### Step 9: Determine the Nature of Profit or Loss
Since the result is positive, it indicates a profit of Rs 25.20.

### Step 10: Calculate Profit Percentage
To find the profit percentage:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 = \left( \frac{25.20}{900} \right) \times 100 \]
\[ = \frac{2520}{900} = 2.8\% \]

### Final Answer
The profit percentage when selling the article for Rs 925.20 is **2.8%**.

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