A shipment of watermelons weighs 100 kilos and is made up of 99% water. After several days in the sun, it is still the same cargo, but now it is made up of 98% water. How much do you weigh now?
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Watermelons in the sun
Thumbnail of misleading percentages: it changes only 1%, and yet the total weight is cut in half. That's why it leaves a mark.
Hints
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- The important part is not the water, but what is not water.
- At first, if 99% is water, the dry matter represents 1% of the total.
- That dry matter does not change its quantity. If it now represents 2% of the total, you can reconstruct the new weight.
Solution
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At first, 99% of 100 kilos is water, so the remaining 1% is dry matter. That means that the dry matter weighs 1 kilo.
After part of the water evaporates, the dry matter still weighs 1 kilo, but now it represents 2% of the total, because the water has dropped to 98%. If 1 kilo is 2% of the new weight, then the total weight must be:
1 / 0.02 = 50 kilos So the shipment now weighs 50 kilos.
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