To determine the rate of markdown that Workwear Station can offer and still break even on the reduced price, we need to consider both the markup and the profit margin.

Here's how we can solve the problem:

Given Information:

• Markup on cost: $60\%$
• Profit margin (percentage of cost): $22\%$

Step 1: Relation between Markup and Selling Price

The formula for the selling price based on cost and markup is: $S = C \times (1 + \text{Markup})$ where:

• $S$ is the selling price,
• $C$ is the cost,
• Markup is 60%.

Thus, the selling price $S$ becomes: $S = C \times (1 + 0.60) = 1.6 \times C$

Step 2: Breakeven Condition

To break even, the reduced selling price must equal the cost, because the company is not making a profit at the breakeven point. So, the reduced selling price, $S(\text{reduced})$, must equal $C$.

Step 3: Determine the Rate of Markdown

We know that: $S(\text{reduced}) = S \times (1 - \text{Rate of Markdown})$

Since the reduced price is equal to the cost ($S(\text{reduced}) = C$), we substitute this into the equation: $C = 1.6 \times C \times (1 - \text{Rate of Markdown})$

Now, divide both sides of the equation by $C$ (assuming $C \neq 0$): $1 = 1.6 \times (1 - \text{Rate of Markdown})$

Solve for the rate of markdown: $\frac{1}{1.6} = 1 - \text{Rate of Markdown}$

$\text{Rate of Markdown} = 1 - \frac{1}{1.6} = 1 - 0.625 = 0.375$

Step 4: Express the Rate of Markdown as a Percentage

The rate of markdown is $0.375$, or $37.5\%$.

Final Answer:

The rate of markdown that Workwear Station can offer and just break even is 37.5%.

Would you like further explanation or have any questions?

Here are 5 related questions for further practice:

1. If Workwear Station increased its markup to 70%, what would the new breakeven markdown be?
2. How does a 50% markdown affect the profit when the markup is 60%?
3. What is the profit margin when the markdown is 25%?
4. If the cost of an item is $100, what is the breakeven reduced price after a 40% markdown?
5. How does a markdown impact overall sales volume and profitability in retail?

Tip: Understanding the relationship between markup, cost, and markdown is essential for calculating profitability and pricing strategy in retail businesses.