How many liters of $20\%$ alcohol solution should be added to $40$ liters of a $50\%$ alcohol solution to make a $30\%$ solution?

Using the rule of alligation, the ratio of the 20% solution to the 50% solution is (50 minus 30) to (30 minus 20), which is 20 to 10, or 2:1. Since one part corresponds to the given 40 liters of the 50% solution, you need two parts of the 20% solution. Multiplying 40 by 2 gives 80 liters.

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