dealer sells his goods sells his goods at 20% loss on cost price but uses 40% less weight. What
is his percentage profit or loss?

Let's analyze the situation step by step:

1. **Cost Price (CP) and Loss Percentage:**
   - The dealer sells his goods at a 20% loss on the cost price. This means he sells the goods for 80% of the cost price.
   - Let the cost price of the goods be \( C \).

2. **Selling Price (SP):**
   - Since he sells at a 20% loss, the selling price would be:
   \[
   \text{SP} = 0.8 \times C
   \]

3. **Weight Reduction:**
   - He uses 40% less weight. So, if the original weight is \( W \), he now uses only 60% of the original weight, which is \( 0.6W \).

4. **Actual Selling Price per Unit Weight:**
   - Since the weight is reduced by 40%, the price he effectively charges per unit of weight increases. The new price per unit weight is:
   \[
   \text{New Price per Unit Weight} = \frac{\text{SP}}{0.6W}
   \]
   Since the original cost per unit weight was \( \frac{C}{W} \), the new effective price per unit weight becomes:
   \[
   \text{New Price per Unit Weight} = \frac{0.8C}{0.6W} = \frac{4}{3} \times \frac{C}{W}
   \]

5. **Effective Profit or Loss:**
   - The dealer effectively sells at \( \frac{4}{3} \) times the cost per unit weight. This means he is selling at a 33.33% gain on the cost per unit weight.

Therefore, the dealer makes a **33.33% profit**.

Would you like more details or have any questions? 

Here are 5 related questions you might find interesting:
1. How would the profit percentage change if the dealer used 50% less weight?
2. What would happen to the profit/loss percentage if the dealer sold at a 10% loss instead?
3. How does the profit percentage vary with different weight reductions?
4. If the dealer sold at the cost price but used 30% less weight, what would be his profit percentage?
5. How would a 25% reduction in weight affect the profit percentage if he sold at a 15% loss?

**Tip:** Always consider the effect of weight reduction or increase when calculating profit or loss in such scenarios.

Understand how to calculate the percentage profit or loss of a dealer who sells goods at a 20% loss on cost price but uses 40% less weight. Explore the step-by-step solution and learn about the impact of weight reduction on profit margins.

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