Loss incurred by selling an article for Rs 800 is 23% more than profit gained by selling same article for Rs 1246 Find the cost price of this article?

Answer

To find the cost price of the article based on the information given, we can follow these steps:

### Step 1: Define Variables
Let:
- CP = Cost Price of the article
- SP1 = Selling Price when sold at a loss = Rs 800
- SP2 = Selling Price when sold at a profit = Rs 1246

### Step 2: Calculate Loss and Profit
1. **Loss when sold for Rs 800**:
\[ \text{Loss} = CP - SP1 = CP - 800 \]

2. **Profit when sold for Rs 1246**:
\[ \text{Profit} = SP2 - CP = 1246 - CP \]

### Step 3: Set Up the Equation
According to the problem, the loss incurred by selling the article for Rs 800 is 23% more than the profit gained by selling it for Rs 1246. Therefore, we can write the equation as:
\[ CP - 800 = 1.23 \times (1246 - CP) \]

### Step 4: Simplify the Equation
Now, let's simplify the equation:
1. Expand the right side:
\[ CP - 800 = 1.23 \times 1246 - 1.23 \times CP \]
\[ CP - 800 = 1539.18 - 1.23CP \]

2. Combine like terms:
\[ CP + 1.23CP = 1539.18 + 800 \]
\[ 2.23CP = 2339.18 \]

### Step 5: Solve for CP
Now, divide both sides by 2.23 to find CP:
\[ CP = \frac{2339.18}{2.23} \approx 1052.00 \]

### Conclusion
Thus, the cost price of the article is approximately Rs 1052.00.

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