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!