A person bought some article at rate of 11 for Rs 10 and bought same number of articles at the rate of 9 for Rs 10. And sold all the stock at the rate of 1 for Rs 1. Find the profit or loss %.

Answer

To solve the problem step by step, we will break down the purchases and sales of the articles.

### Step 1: Calculate the number of articles purchased
- The person buys articles at two different rates:
1. **First Purchase:** 11 articles for Rs 10
2. **Second Purchase:** 9 articles for Rs 10

Let's assume the person buys the same number of articles in both cases. To find a common number of articles, we can take the LCM of 11 and 9, which is 99.

### Step 2: Calculate the total cost for each purchase
- **First Purchase:**
- To buy 99 articles at the rate of 11 articles for Rs 10:
- Number of sets of 11 in 99 = 99 / 11 = 9
- Total cost = 9 sets × Rs 10 = Rs 90

- **Second Purchase:**
- To buy 99 articles at the rate of 9 articles for Rs 10:
- Number of sets of 9 in 99 = 99 / 9 = 11
- Total cost = 11 sets × Rs 10 = Rs 110

### Step 3: Calculate the total cost of all articles
- Total cost = Cost of first purchase + Cost of second purchase
- Total cost = Rs 90 + Rs 110 = Rs 200

### Step 4: Calculate the total number of articles purchased
- Total articles = 99 (from the first purchase) + 99 (from the second purchase) = 198 articles

### Step 5: Calculate the selling price
- The person sells all articles at the rate of 1 article for Rs 1.
- Selling price for 198 articles = 198 articles × Rs 1 = Rs 198

### Step 6: Calculate profit or loss
- Loss = Total cost - Selling price
- Loss = Rs 200 - Rs 198 = Rs 2

### Step 7: Calculate the loss percentage
- Loss percentage = (Loss / Total cost) × 100
- Loss percentage = (2 / 200) × 100 = 1%

### Final Answer
The person incurs a loss of 1%.

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