In a sale, a shopkeeper reduced the advertised selling price of a dress by 20%. This resulted in a profit of 4% over the cost price of the dress.
What percentage profit would the shopkeeper have made if the dress had then been sold at the original selling price?

Let's solve this step by step.

### Given:
- The shopkeeper reduces the advertised selling price by 20%.
- After the reduction, the shopkeeper still makes a profit of 4% over the cost price.

Let:
- $ \text{Original Selling Price} = S $
- $ \text{Cost Price} = C $
- The reduced selling price after the 20% reduction is $ S - 0.2S = 0.8S $.

Since the shopkeeper makes a 4% profit on the cost price when selling at the reduced price:

\[
0.8S = C + 0.04C = 1.04C
\]

### Step 1: Express $ S $ in terms of $ C $
From the equation above:
\[
0.8S = 1.04C
\]

Solving for $ S $:
\[
S = \frac{1.04C}{0.8} = 1.3C
\]

Thus, the original selling price $ S $ is 1.3 times the cost price.

### Step 2: Calculate the profit percentage at the original selling price
If the dress had been sold at the original selling price $ S = 1.3C $, the profit would be:

\[
\text{Profit} = S - C = 1.3C - C = 0.3C
\]

The profit percentage is:

\[
\text{Profit Percentage} = \frac{\text{Profit}}{\text{Cost Price}} \times 100 = \frac{0.3C}{C} \times 100 = 30\%
\]

### Final Answer:
The shopkeeper would have made a **30% profit** if the dress had been sold at the original selling price.

Would you like more details on any part of the solution?

Here are 5 related questions:
1. What would be the new profit if the reduction were 10% instead of 20%?
2. How would the selling price change if the profit percentage increased to 10% instead of 4%?
3. What if the shopkeeper incurred a loss of 5% on the dress after the 20% reduction? How would that affect the calculations?
4. How does a change in cost price impact the overall profit margin in percentage terms?
5. Can we determine the exact cost price if the selling price was $150?

**Tip**: Always calculate the cost price first to simplify profit margin-related problems.

In a sale, a shopkeeper reduced the advertised selling price of a dress by 20%. This resulted in a profit of 4% over the cost price of the dress. What percentage profit would the shopkeeper have made if the dress had then been sold at the original selling price?

Learn how to calculate the profit percentage if a dress is sold at its original price after a 20% reduction, using key profit and percentage formulas. This step-by-step guide is perfect for students in Grades 8-10 looking to strengthen their understanding of profit and loss concepts.

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