A trader cheats both his supplier and customer by using faulty weights. When he buys from the supplier, he takes 10% more than the indicated weight. When he sells to his customer, he gives the customer a weight such that 10% of that is added to the weight, the weight claimed by the trader is obtained. If he charges the cost price of the weight that he claims, find his profit percentage.

Let's analyze the problem step by step.

### Step 1: Understanding the trader's actions

1. **Buying from the supplier:**
   - The trader is supposed to buy 1 unit of weight from the supplier.
   - However, he cheats and takes 10% more. 
   - Thus, the actual weight he receives from the supplier is \( 1 + 0.1 = 1.1 \) units.

2. **Selling to the customer:**
   - When selling, the trader gives the customer a weight \( x \) such that the indicated weight is \( x + 0.1x = 1.1x \).
   - He claims this weight as 1 unit.

### Step 2: Calculate the effective weight sold by the trader
- From the trader's perspective, the weight \( x \) that corresponds to 1 unit on his faulty scale is:
  \[
  1.1x = 1 \quad \text{so} \quad x = \frac{1}{1.1} = \frac{10}{11}
  \]
- This means the customer actually receives \( \frac{10}{11} \) units.

### Step 3: Calculate the profit percentage
1. **Cost Price:**
   - The trader buys 1.1 units from the supplier, but the cost price he considers is for 1 unit.

2. **Selling Price:**
   - The trader sells \( \frac{10}{11} \) units but charges for 1 unit.

3. **Profit Calculation:**
   - The cost price (CP) for 1 unit is proportional to 1.1 units.
   - The selling price (SP) for \( \frac{10}{11} \) units is proportional to 1 unit.

   - Therefore, the profit percentage is calculated as:
     \[
     \text{Profit Percentage} = \left(\frac{\text{SP} - \text{CP}}{\text{CP}}\right) \times 100
     \]

     Given:
     \[
     \text{CP} = 1.1 \quad \text{and} \quad \text{SP} = 1
     \]
     Profit percentage:
     \[
     \text{Profit Percentage} = \left(\frac{1 - \frac{10}{11}}{\frac{10}{11}}\right) \times 100
     = \left(\frac{\frac{11 - 10}{11}}{\frac{10}{11}}\right) \times 100
     = \left(\frac{\frac{1}{11}}{\frac{10}{11}}\right) \times 100
     = \left(\frac{1}{10}\right) \times 100 = 10\%
     \]

### Conclusion
The trader's profit percentage is **10%**.

Do you want details or have any questions?

Here are five related questions for practice:
1. If the trader gave the exact weight to the customer, what would be the profit percentage?
2. How much profit would the trader make if he bought and sold 100 units?
3. What would be the profit percentage if the trader took 20% more weight from the supplier?
4. If the trader sells at 5% above the cost price in addition to the cheating, what is the new profit percentage?
5. How does the profit percentage change if the faulty weights were adjusted by 5% instead of 10%?

**Tip:** To avoid being cheated, always cross-check the weights and measures with standardized equipment.

Understand how a trader's profit percentage is calculated when using faulty weights to cheat both suppliers and customers. This math problem involves arithmetic and percentage calculations, focusing on profit and loss concepts. Suitable for students in Grades 7-9.

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