Stacked Discounts: Why 20% Plus 10% Isn't 30% Off

"Extra 10% off sale prices!" sounds as if it adds to an existing 20% discount to make 30%. It doesn't, and knowing why helps you compare deals in seconds.

Discounts multiply, they don't add

The second discount is taken from the already-reduced price. So instead of adding percentages, multiply what you pay at each step:

For a $100 item at 20% off, then 10% off: 100 × 0.80 × 0.90 = $72. That's a total discount of 28%, not 30%.

Does the order matter?

Not for two percentage discounts: 100 × 0.90 × 0.80 is also $72. It does matter when one of them is a fixed amount. A $10-off coupon is worth more if it's applied after a 20% discount: (100 × 0.8) − 10 = $70, versus (100 − 10) × 0.8 = $72 if it's applied first.

Finding the original price

If a receipt shows you paid $72 after 20% and 10% off, divide by both multipliers: 72 ÷ 0.8 ÷ 0.9 = $100.

Compare by unit price

A bigger pack on sale isn't always cheaper. Divide the price by the quantity to get a price per unit:

A 500 g bag for $3.50 costs $0.70 per 100 g. A 1.2 kg bag for $7.80 costs $0.65 per 100 g, so the bigger bag wins, but only if you'll use it before it goes off.

Quick checks at the till

• 25% off: you pay three quarters of the price.
• "Buy one, get one half price" on two equal items is 25% off overall.
• "Buy two, get one free" is 33.3% off each item when you take all three.