Step 1 :The net price that the retailer pays for the bike is $111.56.
Step 2 :The price after the first discount of 15% is calculated by dividing the net price by 0.85, which gives $131.25 (rounded to the nearest cent).
Step 3 :The list price, which is the price before the second discount of 25%, is calculated by dividing the price after the first discount by 0.75, which gives $175.00.
Step 4 :Final Answer: The list price of the bike is \(\boxed{175.00}\).