The watermelon that lost half its weight

Question

A pile of fresh watermelon weighs 100 kg and is 99 per cent water by weight. It is left in the sun for a day and some of the water evaporates. Afterwards it is 98 per cent water. How much does the pile weigh now? Most people guess about 99 kg. Check that guess.

Accepted Answer

50 kg. Track the solids. At the start the pile is 99 per cent water, so 1 per cent of it, 1 kg, is solid matter (sugar, fibre, seeds). Drying removes only water, so the pile still contains exactly 1 kg of solids afterwards. Use the new percentage. After drying, water is 98 per cent of the weight, so solids are 2 per cent. If 1 kg is 2 per cent of the total, the total is 1 / 0.02 = 50 kg. Why intuition fails. Going from 99 per cent to 98 per cent water sounds like a tiny change, so people expect a tiny change in weight. But the meaningful quantity is the solid fraction, which doubled from 1 pe…

The watermelon that lost half its weight

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