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 given the conditions of loss and profit, we can follow these steps:

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

### Step 2: Determine Profit and Loss
1. The selling price (SP) when sold at a loss is Rs 800.
2. The selling price (SP) when sold at a profit is Rs 1246.

### Step 3: Calculate Loss and Profit
- Loss incurred when selling for Rs 800:
\[ \text{Loss} = CP - SP = CP - 800 \]

- Profit gained when selling for Rs 1246:
\[ \text{Profit} = SP - CP = 1246 - CP \]

### Step 4: Relate Loss and Profit
According to the problem, the loss incurred is 23% more than the profit gained. Therefore, we can write:
\[ CP - 800 = 1.23 \times (1246 - CP) \]

### Step 5: Expand the Equation
Now, let's expand and rearrange the equation:
\[ CP - 800 = 1.23 \times 1246 - 1.23 \times CP \]
\[ CP - 800 = 1530.58 - 1.23CP \]

### Step 6: Combine Like Terms
Now, let's bring all terms involving \( CP \) to one side:
\[ CP + 1.23CP = 1530.58 + 800 \]
\[ 2.23CP = 2330.58 \]

### Step 7: Solve for Cost Price
Now, divide both sides by 2.23 to find \( CP \):
\[ CP = \frac{2330.58}{2.23} \approx 1046.00 \]

### Conclusion
Thus, the cost price of the article is approximately Rs 1046.

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