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.