Here are the formulas for each of the requested terms related to pricing and profitability:

1. Original Price (Cost Price, $C$): The original price is the price at which the item is purchased or manufactured.
   $C = \text{Cost Price}$

2. Selling Price ($S$): The selling price is the price at which the item is sold to customers.
   $S = \text{Selling Price}$

3. Markup ($M$): Markup is the difference between the selling price and the original price (cost price).
   $M = S - C$

4. Markup Rate ($MR$): The markup rate is the percentage increase of the cost price to reach the selling price.
   $MR = \left( \frac{M}{C} \right) \times 100 = \left( \frac{S - C}{C} \right) \times 100$

5. Markdown ($Md$): Markdown refers to the reduction in the selling price from the original or listed price.
   $Md = \text{Original Selling Price} - \text{New Selling Price}$

6. Markdown Rate ($MdR$): Markdown rate is the percentage decrease from the original selling price.
   $MdR = \left( \frac{Md}{\text{Original Selling Price}} \right) \times 100$

7. Gross Margin ($GM$): Gross margin is the difference between the selling price and the cost price, similar to markup, but focusing on profit.
   $GM = S - C$

8. Gross Margin Rate ($GMR$): The gross margin rate is the percentage of the selling price that is profit.
   $GMR = \left( \frac{GM}{S} \right) \times 100 = \left( \frac{S - C}{S} \right) \times 100$

Summary of Formulas:

• Original Price: $C$
• Selling Price: $S$
• Markup: $M = S - C$
• Markup Rate: $MR = \left( \frac{S - C}{C} \right) \times 100$
• Markdown: $Md = \text{Original Selling Price} - \text{New Selling Price}$
• Markdown Rate: $MdR = \left( \frac{Md}{\text{Original Selling Price}} \right) \times 100$
• Gross Margin: $GM = S - C$
• Gross Margin Rate: $GMR = \left( \frac{S - C}{S} \right) \times 100$

Would you like more detailed explanations or specific examples for any of these terms?

Here are 5 relative questions:

1. How does increasing the markup rate affect the gross margin rate?
2. What happens to the selling price if you apply a markdown after markup?
3. Can the markdown rate exceed 100%? Why or why not?
4. How is gross margin different from profit margin?
5. Why might a business choose a lower markup rate but aim for a higher gross margin rate?

Tip: Monitoring both markup and markdown rates helps businesses balance profits and competitiveness effectively.