The rule
final = price × (1 − d₁) × (1 − d₂)
Why it works
A discount multiplies the price by what is left of it. Take 30 % off and you keep 70 %, so you multiply by 0.7. Apply a second discount and it works on the already reduced price, not on the original.
How to do it by hand
- Turn each discount into what remains: 30 % off leaves 0.7
- Multiply the price by the first factor
- Multiply that result by the second factor
- The saving is the original price minus the final one
What is worth knowing
Successive discounts never add. 30 % and then 20 % is not 50 % off but 44 %, because the second discount applies to a smaller price. The gap grows with the size of the discounts: two 50 % discounts leave 25 % of the price, not zero. This is worth knowing in both directions — shops use it to make stacked offers sound better than they are, and it is also why a discount followed by a tax does not cancel out even when the percentages match.