# Fruit Seller’s Paradox

**Fruit Seller’s Paradox- **Each of two apple women had 30 apples for sale. The first sold hers at the rate of 2 for a nickel, the second at the rate of 3 for a nickel. At the end of the day their respective receipts were 75 cents and 50 cents, or $1.25 in all.

The next day the women decided to do business together, so they pooled their 60 apples and sold them at the rate of 5 for a dime (2 for a nickel plus 3 for a nickel). Upon counting their joint receipts at the end of the day they were dismayed to find that they had only $1.20. They searched all about them for that other nickel, and wound up by bitterly accusing each other of having taken it. Where was it? (1 Nickel = 5 Cents)

4 Comments

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The cost of each apple at 2 for a nickle is 2.5 cents a peice, while at 3 for a nickle is 1.666 ~ 1.67 cents a peice. To get the original $1.25 for selling all 60 apples, they must be sold at (1.67+2.5)/2 = 2.08 cents a peice. However, the 60 apples are sold at 2 cents a peice. Meaning a loss of 0.08 * 60 = 4.8 cents which is approximately a nickle. And thus the mystery of the missing nickle is solved

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