A merchant claim to make profit of 12.5% on
his sales but actually makes 25% by using false
weight when he professes to sell 1kg, how
much does he actually sale?


To solve this problem, let's analyze it step-by-step:

1. **Understanding the Problem**:
   - The merchant claims to make a profit of 12.5% on his sales.
   - In reality, he makes a 25% profit by using a false weight.
   - When he claims to sell 1 kg, he is actually selling less than 1 kg. We need to find the actual weight he sells.

2. **Let the Actual Weight be \(x\) kg**:
   - The merchant claims he is selling 1 kg, but he is actually selling \(x\) kg.
   - To calculate the profit due to false weight, we know that his actual profit is 25%.

3. **Calculating Profit Due to False Weight**:
   - Profit percentage due to false weight is given by:
   \[
   \text{Profit Percentage} = \left( \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \right) \times 100
   \]
   - Let the cost price (CP) of 1 kg be \(C\). The merchant sells \(x\) kg for the selling price (SP) of 1 kg, so:
   \[
   \text{SP} = C
   \]
   - The actual cost for \(x\) kg is \(x \cdot C\).
   - The profit he actually makes is:
   \[
   \text{Profit} = C - xC = C(1 - x)
   \]

   Given that the profit percentage is 25%, we have:
   \[
   \frac{C(1 - x)}{xC} \times 100 = 25
   \]

4. **Solving for \(x\)**:
   \[
   \frac{1 - x}{x} \times 100 = 25
   \]

   Simplifying, we get:
   \[
   \frac{1 - x}{x} = 0.25
   \]

   Cross multiplying, we get:
   \[
   1 - x = 0.25x
   \]

   \[
   1 = 1.25x
   \]

   \[
   x = \frac{1}{1.25}
   \]

   \[
   x = 0.8
   \]

5. **Conclusion**:
   - The merchant actually sells **0.8 kg** when he claims to sell 1 kg.

### Summary
The merchant is selling 0.8 kg instead of 1 kg, resulting in a 25% profit due to using false weights.

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Would you like to see more details or have any questions? Here are some related topics:

1. How to calculate profit percentage for different scenarios.
2. The impact of false measurements on overall profit margins.
3. Real-life applications of profit and loss calculations in business.
4. Exploring ethical business practices regarding weights and measures.
5. Solving problems involving cost price, selling price, and profit using algebra.

**Tip:** Understanding the basics of percentage calculations is crucial for solving many real-world problems, especially in commerce and economics!

A merchant claims to make a profit of 12.5% on his sales but actually makes 25% by using false weight when he professes to sell 1kg, how much does he actually sell?

Discover how to calculate the actual weight sold by a merchant who claims to make a profit of 12.5% but actually makes 25% by using false weights. This problem involves key concepts in profit and loss, algebra, and percentage calculations, and is suitable for students in Grades 8-10.

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