Why Stacked Discounts Don't Add Up the Way They Seem To
Two stacked percentage discounts don't add up to their sum, because the second discount applies to the already-reduced price, not the original — "20% off, then an extra 10% off" results in a combined discount of 28%, not 30%, since the second 10% is calculated on a smaller base than the original price.
This is a genuinely common point of confusion at checkout, and it's worth understanding exactly why the intuitive "just add the percentages" approach falls short.
A worked example
A $100 item with 20% off brings the price to $80. An additional 10% off that $80 (not the original $100) is $8, bringing the price to $72 — a total combined discount of 28% off the original price, not the 30% that simply adding 20% and 10% would suggest.
Why the gap grows with larger discounts
The difference between the "naive sum" and the actual combined discount grows larger as the individual discount percentages increase — two 50% discounts stacked don't produce 100% off (a free item); they produce 75% off, since the second 50% only applies to the already-halved price.
The correct way to calculate a combined discount
Applying each discount in sequence to the progressively reduced price — rather than adding the percentages together and applying that sum once — always gives the mathematically correct final price, and is exactly how the worked example above was calculated.