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The problem provided is asking to determine the original price of an item, given the following conditions:

- The selling price has a 20% discount applied.
- Despite the discount, the seller still gains a profit of 30% over the cost.
- The cost of the item is **S/ 1600**.

Let’s break this down step by step.

### Step-by-step breakdown:

1. **Let the original price of the item be \( P \)**.

2. **20% discount**: After applying the 20% discount, the price becomes 80% of the original price:
   \[
   \text{Discounted price} = 0.8P
   \]

3. **Profit condition**: Despite the discount, the seller still gains 30% over the cost of S/ 1600. Therefore, the discounted price is 130% of the cost:
   \[
   \text{Discounted price} = 1.3 \times 1600 = 2080
   \]

4. **Set up the equation**: From the two expressions for the discounted price, we have:
   \[
   0.8P = 2080
   \]

5. **Solve for \( P \)**:
   \[
   P = \frac{2080}{0.8} = 2600
   \]

Thus, the original price of the item is **S/ 2600**.

### Final Answer:
- The correct answer is \( \boxed{D} \) **S/ 2600**.

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Do you need further details or have any other questions?

Here are 5 related questions to practice with:

1. If the cost of another item is S/ 2000 and a 25% discount is applied but a 40% profit is made, what is the original price?
2. How would the equation change if the discount was 15% instead of 20%?
3. If the cost price were S/ 1800 instead of S/ 1600, what would the original price be with the same conditions?
4. What is the relationship between cost price, discount, and profit in pricing strategies?
5. How do percentage changes (like profit or discount) affect the final selling price?

**Tip:** When working with percentage-based problems, always set up clear relationships between the given quantities using algebraic expressions before solving.

Determinar el precio fijado de un artículo, sabiendo que al venderlo se hace una rebaja del 20% y aún así se gana el 30% de su costo; sabiendo además que su precio de costo es de S/ 1 600

Learn how to determine the original price of an item given that a 20% discount is applied and a 30% profit is made on a cost of S/ 1,600. Detailed step-by-step solution provided for high school level students.

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