Two discounts, one number, 20% off then 15% off

Question

A jacket is marked 20\% off, and at checkout a further 15\% is taken off the reduced price. Solve in your head. What single discount is this equivalent to? Aim: under 10 seconds.

Accepted Answer

Work with the multipliers that survive each discount: 0.80 	imes 0.85 = 0.68. Mental route for 0.8 	imes 0.85: 8 	imes 85 = 680, then place the decimal. You keep 68\%, so the combined discount is 1 - 0.68 = 32\%. Not 35\%, the second discount acts on an already-reduced price, so the chain is always milder than the sum. Takeaway. Percentage changes compose by multiplying retention factors: (1-a)(1-b) = 1 - a - b + ab. The correction term +ab (here 0.03) is exactly why "add the percentages" is wrong, and quoting it is how you show an interviewer you actually understand the structure.

Two discounts, one number, 20% off then 15% off

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