The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?

Options

A. Rs. 2000
B. Rs. 2200
C. Rs. 2400
D. None of these

Answer

To solve the problem step by step, we will first establish the relationship between the selling prices, the cost price, and the percentage profit and loss.

### Step 1: Define Variables
Let the Cost Price (CP) of the article be \( x \).

### Step 2: Set Up Equations for Selling Prices
According to the problem:
- Selling Price (SP) when sold for Rs. 1920 results in a profit.
- Selling Price (SP) when sold for Rs. 1280 results in a loss.

The percentage profit when sold for Rs. 1920 can be expressed as:
\[ \text{Percentage Profit} = \frac{SP - CP}{CP} \times 100 = \frac{1920 - x}{x} \times 100 \]

The percentage loss when sold for Rs. 1280 can be expressed as:
\[ \text{Percentage Loss} = \frac{CP - SP}{CP} \times 100 = \frac{x - 1280}{x} \times 100 \]

### Step 3: Set the Profit Equal to Loss
According to the problem, the percentage profit is equal to the percentage loss:
\[ \frac{1920 - x}{x} \times 100 = \frac{x - 1280}{x} \times 100 \]

We can simplify this equation by cancelling out 100 from both sides:
\[ \frac{1920 - x}{x} = \frac{x - 1280}{x} \]

### Step 4: Cross Multiply
Cross multiplying gives us:
\[ 1920 - x = x - 1280 \]

### Step 5: Solve for x
Now, rearranging the equation:
\[ 1920 + 1280 = 2x \]
\[ 3200 = 2x \]
\[ x = \frac{3200}{2} = 1600 \]

So, the Cost Price (CP) of the article is Rs. 1600.

### Step 6: Calculate Selling Price for 25% Profit
To find the selling price (SP) for a 25% profit, we can use the formula:
\[ SP = CP + \text{Profit} \]
Where Profit = 25% of CP:
\[ \text{Profit} = \frac{25}{100} \times 1600 = 400 \]

Thus, the Selling Price for 25% profit is:
\[ SP = 1600 + 400 = 2000 \]

### Final Answer
The article should be sold for Rs. 2000 to make a 25% profit.

---