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A 10 liter mixture of cranberry juice and water contains juice and water in the ratio of 3 : 2. 5 liters of the mixture are removed and replaced with pure juice and the operation is repeated once more. At the end of the two removals and replacements, what is the ratio of juice to water in the resulting mixture?

The initial mixture contains 6 liters of juice and 4 of water. 50% of the mixture is removed each time (5 liters is 50% of 10 liters of initial mixture). This means we have to remove 50% of juice as well as 50% of water. After the first removal of 5 liters it has 3 liters of juice and 2 of water. Adding 5 liters of juice gives us a mixture of 8 liters of juice and 2 of water. Removing 5 liters of the mixture, we have 4 liters of juice and 1 of water. Adding 5 liters of juice again gives us a 9 : 1 ratio of juice to water.

My question is : How do we know that we have to remove 50% of juice as well as 50% of water???

I think you don´t need to wonder about how well the two elements are mixed. Within a mixture problem you assume that the two fluids are of equal concentration. Otherwise you´ll always need answer E : not enough information to answer the question