Up 25%, then down 20%, where do you land?

Question

A stock rises 25\% on Monday, then falls 20\% on Tuesday. Solve in your head. What is the net change over the two days? Aim: under 10 seconds.

Accepted Answer

Chain the multipliers: 1.25 	imes 0.80 = 1.00. Mental route: 1.25 	imes 0.8 = 1.25 	imes 	frac{4}{5} = 	frac{5}{5} = 1. You end exactly where you started, a net change of 0\%. The naive "up 25, down 20, so up 5" is wrong because the 20\% drop applies to the larger Monday price. Here the two effects cancel precisely, because 1.25 = 5/4 and 0.80 = 4/5 are reciprocals. Takeaway. Sequential percentage moves multiply. A +25\% then -20\% is a wash because 	frac54 	imes 	frac45 = 1: whenever the up-factor and down-factor are reciprocals, you return exactly to the start.

Up 25%, then down 20%, where do you land?

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