HMMT 二月 2018 · 冲刺赛 · 第 2 题

HMMT February 2018 — Guts Round — Problem 2

[ 4 ] John has a 1 liter bottle of pure orange juice. He pours half of the contents of the bottle into a vat, fills the bottle with water, and mixes thoroughly. He then repeats this process 9 more times. Afterwards, he pours the remaining contents of the bottle into the vat. What fraction of the liquid in the vat is now water?

解析

[ 4 ] John has a 1 liter bottle of pure orange juice. He pours half of the contents of the bottle into a vat, fills the bottle with water, and mixes thoroughly. He then repeats this process 9 more times. Afterwards, he pours the remaining contents of the bottle into the vat. What fraction of the liquid in the vat is now water? Proposed by: Farrell Eldrian Wu 5 Answer: 6 All the liquid was poured out eventually. 5 liters of water was poured in, and he started with 1 liter of 5 5 orange juice, so the fraction is = . 1+5 6