Two discounts, 30% off then 10% off

Question

A pair of boots is marked 30\% off, and at the register another 10\% comes off the reduced price. Solve in your head. What single discount is this equivalent to? Aim: under 10 seconds.

Accepted Answer

Multiply the retention factors left after each cut: 0.70 	imes 0.90 = 0.63. Mental route: 7 	imes 9 = 63, then place the decimal. You keep 63\%, so the combined discount is 1 - 0.63 = 37\%. Not 40\%: the 10\% acts on an already-reduced price, so the chain is milder than the sum. Takeaway. Discounts compose by multiplying what remains: (1-a)(1-b) = 1 - a - b + ab. The +ab term (here 0.03) is exactly why "add the percentages" overshoots, and naming it signals you understand the structure.

Two discounts, 30% off then 10% off

Your answer

More Mental Math questions