Math CentralQuandaries & Queries


Question from Joanna, a student:

How many liters of water must evaporate from 40 liters of a 10% salt solution to make a 25% salt solution?


If 10% of the 40 liters is salt then the amount of salt is 0.10 × 40 = 4 liters. The water evaporates until this 4 liters makes up 25% of the volume. What is the total volume if 25% of this total is 4 liters?



Many questions of this type are unrealistic, because solutions and mixtures often take up less space than their constituent substances do.

But making the false assumption that math books have made for centuries that volumes are additive, first find out how much salt and how much water are represented by your "40 liters of a 10% salt solution".

Now figure out how much water would go with that much salt in a 25% salt solution. How much less is that?

The general rule here: For almost any mixture problem, first convert everything to absolute quantities of pure substances.

Good Hunting!

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