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Interview prep / Brainteaser/Logic

Fair split of 8 dollars for shared wheat

Question

Three housemates share all food equally. Josiah contributes 55 bushels of wheat, Charles contributes 33, and Michael contributes nothing but instead pays $8, to be divided between Josiah and Charles fairly. How much more of the money should Josiah get than Charles?

Short answer

$6 more. Each person eats 83\tfrac83 bushels, so Josiah gives up 5−83=735-\tfrac83=\tfrac73 and Charles gives up 3−83=133-\tfrac83=\tfrac13 to Michael. The $8 buys 83\tfrac83 bushels, i.e. $1 per third of a bushel, so Josiah gets $7 and Charles $1.

Adapted from OpenQuant; question and answer rewritten by SelfMadeQuant.com.

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