money
did you know two twenty-percent discounts do not make forty?
the second discount works on a price that has already shrunk.
20% + 20% → 36%
overall saving when applied successively
both reductions apply to the current price, with no other fees or conditions.
- £100
- £80 after first discount
- £64 after second
the idea
take 20% off a £100 item and it costs £80. take another 20% off and it costs £64. the total saving is £36, or 36%, because the second discount applies to the reduced price.
how it works
a 20% discount leaves 80% of the price. multiplying by 0.8 twice leaves 64%. subtract that remaining fraction from one to get the overall discount.
go deeper
which number is the percentage of?
take 20% off a £100 item and it costs £80. take another 20% off and it costs £64. the total saving is £36, or 36%, because the second discount applies to the reduced price.
a percentage needs a base. the first 20% refers to £100; the second refers to £80. treating both as £20 discounts silently changes the second base back to the original price.
follow what remains
a 20% discount leaves 80% of the price. multiplying by 0.8 twice leaves 64%. subtract that remaining fraction from one to get the overall discount.
in this simple model, applying 10% and then 20% gives the same result as 20% and then 10%, because 0.9 × 0.8 equals 0.8 × 0.9. fixed-amount vouchers and special conditions can change that.
how do any two percentage discounts combine?
write discounts a and b as fractions. the remaining price fraction is (1 − a)(1 − b), so the combined discount is a + b − ab.
combined discount = 1 − (1 − a)(1 − b); 1 − 0.8² = 0.36
does a twenty-percent rise undo the discount?
- no. £80 increased by 20% becomes £96. getting from £80 back to £100 requires a 25% increase.
- this is arithmetic for stated successive discounts. actual checkout rules, rounding, and which offers can combine determine a real purchase price.
sources & further reading
concepts: percentages · multiplicative change · remaining fractions
2 minute read