The Watermelon Puzzle

An amusing puzzle appears in a recent book by John A. Adam (2013). The answer is very surprising. The book argues in terms of simultaneous equations. A simpler argument, using the diagram below, should make all clear.

The Watermelon Puzzle.

A farmer brings a load of watermelons to the market. Before he sets out, he measures the total weight and the percentage water content. He finds that the total weight is 100kg and the water content is 99%.

The weather is hot, so his load loses some moisture en route. He checks the water content when he arrives at the market: it has dropped to 98%.

QUESTION: What is the total weight of the load on arrival at market ?

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Most people would guess something around 98 or 99kg.

This is very wide of the mark.

Think again before you read on.

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Initially there is 99% water and so 1% pith. At the market, there is 98% water, and therefore 2% pith. The percentage of pith has doubled. But the actual amount of pith is unchanged. The only way this can happen is if the total weight is halved!

ANSWER: The weight of the load on arrival at market is 50kg.

The answer is quite surprising. The illustration below should make everything clear:

Figure:  Weights. Upper panel: Total weight 100kg: 1kg pith (black) and 99kg water (grey). Lower panel: Total weight 50kg: 1kg pith (black) and 49kg water (grey).  Percentages. Upper panel: 99kg water makes 99%. 1kg pith makes 1%. Lower panel: 49kg water makes 98%. 1kg pith makes 2%. The weight of pith does not change, but the percentage doubles.

Upper panel: Total weight 100kg: 1kg pith (black, 1%) and 99kg water (grey, 99%). Lower panel: Total weight 50kg: 1kg pith (black, 2%) and 49kg water (grey, 98%). The weight of pith does not change, but the percentage doubles. The total weight is halved.

Source:

John A. Adam, 2013: X and the City: Modeling Aspects of Urban Life. Princeton Univ. Press. 336 pp. Paper ISBN: 9780691162324. Cloth ISBN: 9780691154640.


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