Raise 25% then take 20% off

A product originally priced at 400 yuan is first marked up by 25%, then sold at a 20% discount. Find the final selling price.

Step-by-step

1. 400 × (1 + 0.25) = 500
   Price rise: multiply by (1 + increase rate)
2. 500 × (1 − 0.2) = 400
   Price cut: multiply by (1 − decrease rate)

Why it works

Two consecutive percentage changes cannot be combined by simply adding the percentages: the base for the markup and the discount are different. The first change applies to the original price, and the second applies to the marked-up price. The correct method is to multiply step by step by (1 + growth rate) or (1 − discount rate). In this problem, the two changes exactly cancel each other out, which is a common trap and also a self-check point.

Common mistakes

• Subtracting 25% and 20% to get 5%, then directly calculating it as 95% of the original price.
• Treating a 20% discount as subtracting 8% instead of multiplying by 0.8.
• Applying the second discount to the original price rather than to the marked-up price.