Clearance stacking, 40% off then 25% off

Question

A coat is 40\% off, and a clearance coupon takes a further 25\% 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: 0.60 	imes 0.75 = 0.45. Mental route: 0.75 is three-quarters, and three-quarters of 0.60 is 0.60 - 0.15 = 0.45. You keep 45\%, so the combined discount is 1 - 0.45 = 55\%. Not 65\%: the 25\% coupon acts on the already-discounted price, so the chain undershoots the naive sum by the +ab = 0.10 correction. Takeaway. Stacked discounts multiply what survives: keeping 60\% then 75\% leaves 45\%, a 55\% total cut, not 65\%. Converting the second discount to a fraction (25\% = 	frac14 off, so 	frac34 kept) makes the arithmetic instant.

Clearance stacking, 40% off then 25% off

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