Let's break down the problem step by step:

Step 1: Determine the original selling price.

The cost price of the hard disk is $500. The store has a markup rate of 55% of the selling price. Let the selling price be denoted as $S$.

Since the markup is 55% of the selling price: $\text{Cost price} = S - 0.55S = 0.45S$ The cost price is given as $500: $0.45S = 500$

Now, solve for $S$ (the original selling price): $S = \frac{500}{0.45} = 1111.11$ So, the original selling price is $1111.11.

Step 2: Apply the markdown.

The markdown is 80%, which means the item is sold at 20% of the original price. The reduced price is: $\text{Reduced Price} = 0.20 \times 1111.11 = 222.22$

Final Answer:

The reduced selling price is $222.22.

Would you like further details or have any questions? Here are five related questions:

1. What would the selling price be if the markup rate was 70% instead of 55%?
2. How would the reduced price change if the markdown was only 50%?
3. If the store sells 10 hard-disks at the reduced price, what is the total revenue?
4. How much profit is made per hard disk after the markdown?
5. What is the overall percentage discount from the original selling price to the reduced price?

Tip: Markup and markdown calculations are often based on either cost price or selling price, so pay attention to how these percentages are defined in problems.