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 of the article given that the loss incurred by selling it for Rs 600 is equal to the profit gained by selling it for Rs 1000, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables**:
Let the cost price (CP) of the article be \( CP \).

2. **Understand Loss and Profit**:
- When the article is sold for Rs 600, a loss is incurred. The loss can be expressed as:
\[ \text{Loss} = CP - 600 \]
- When the article is sold for Rs 1000, a profit is gained. The profit can be expressed as:
\[ \text{Profit} = 1000 - CP \]

3. **Set Up the Equation**:
According to the problem, the loss incurred when selling for Rs 600 is equal to the profit gained when selling for Rs 1000:
\[ CP - 600 = 1000 - CP \]

4. **Solve the Equation**:
- Rearranging the equation gives:
\[ CP + CP = 1000 + 600 \]
- This simplifies to:
\[ 2CP = 1600 \]
- Dividing both sides by 2:
\[ CP = \frac{1600}{2} = 800 \]

5. **Conclusion**:
The cost price of the article is Rs 800.

### Final Answer:
The cost price of the article is Rs 800.

---