Loss incurred by selling an article for Rs 600 is equal to profit gained by selling same article for Rs 1000 Find the cost price of this article

Answer

To find the cost price (CP) of the article based on the information provided, we can follow these steps:

### Step 1: Define Variables
Let the cost price of the article be denoted as CP.

### Step 2: Understand Loss and Profit
According to the problem:
- When the article is sold for Rs 600, there is a loss.
- When the article is sold for Rs 1000, there is a profit.

### Step 3: Express Loss and Profit Mathematically
1. **Loss when sold for Rs 600**:
Loss = Cost Price - Selling Price
\[ \text{Loss} = CP - 600 \]

2. **Profit when sold for Rs 1000**:
Profit = Selling Price - Cost Price
\[ \text{Profit} = 1000 - CP \]

### Step 4: Set Up the Equation
According to the problem, the loss incurred by selling at Rs 600 is equal to the profit gained by selling at Rs 1000. Therefore, we can set up the equation:
\[ CP - 600 = 1000 - CP \]

### Step 5: Solve the Equation
1. Rearranging the equation:
\[ CP + CP = 1000 + 600 \]
\[ 2CP = 1600 \]

2. Divide both sides by 2:
\[ CP = \frac{1600}{2} = 800 \]

### Step 6: Conclusion
The cost price of the article is Rs 800.