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 break down the problem step by step to find the trader's profit percentage.

### Step 1: Understanding the buying process
- **Actual weight received from the supplier**: When the trader buys from the supplier, he takes 10% more than the indicated weight.
  - Let the indicated weight be \( W \).
  - The actual weight the trader receives is \( 1.1W \) (since he takes 10% more than \( W \)).

### Step 2: Understanding the selling process
- **Weight sold to the customer**: When the trader sells to the customer, he gives them a weight such that adding 10% of it gives the weight claimed by the trader.
  - Let the weight the trader actually gives to the customer be \( x \).
  - The weight claimed by the trader (after adding 10%) is \( x + 0.1x = 1.1x \).

### Step 3: Cost price and selling price
- **Cost price**: The trader pays the supplier for the indicated weight \( W \), but he actually receives \( 1.1W \).
- **Selling price**: The trader sells to the customer claiming a weight of \( 1.1x \), but he actually gives \( x \).

### Step 4: Profit calculation
The profit percentage is calculated as:

\[
\text{Profit Percentage} = \left( \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \right) \times 100
\]

- **Cost Price**: The cost price for the trader is based on the weight \( W \) which he pays for. Since the actual weight he receives is \( 1.1W \), the cost price per unit of actual weight is:
  
  \[
  \text{Cost Price per unit} = \frac{W}{1.1W} = \frac{1}{1.1} = \frac{10}{11}
  \]

- **Selling Price**: The trader sells \( x \) units but claims it as \( 1.1x \). The selling price per unit of actual weight is \( 1.1 \).

### Step 5: Profit percentage calculation
The profit per unit of actual weight is:

\[
\text{Profit per unit} = \text{Selling Price per unit} - \text{Cost Price per unit} = 1.1 - \frac{10}{11} = 1.1 - 0.9091 = 0.1909
\]

Now, calculate the profit percentage:

\[
\text{Profit Percentage} = \left( \frac{0.1909}{\frac{10}{11}} \right) \times 100
\]

Simplify further:

\[
\text{Profit Percentage} = \left( \frac{0.1909 \times 11}{10} \right) \times 100 = \left( 0.20999 \right) \times 100 = 21\%
\]

Thus, the trader's profit percentage is **21%**.

Would you like more details or have any questions?

### Related Questions:
1. What would be the profit percentage if the trader took 20% more weight from the supplier?
2. How would the profit percentage change if the trader gave only 90% of the claimed weight to the customer?
3. If the supplier increased the weight prices by 15%, how would it affect the trader's profit?
4. How much weight should the trader actually give to maintain a 25% profit margin?
5. What would happen to the profit percentage if the customer caught the trader's cheating and only paid for the actual weight?

### Tip:
When calculating profit percentages in trade, always factor in the difference between actual and claimed values, as this can significantly affect outcomes.

Learn how to calculate a trader's profit percentage when using faulty weights. Understand the process of profit calculation involving cost price, selling price, and the impact of weight manipulation. Suitable for high school students and anyone interested in basic profit calculation in trade.

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