TBR Physics: U-Tube problem

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In this problem, we were given a U-tube with water and solution Z. Here is a picture of the diagram:

The question asks about the density of solution Z, and the answer is: (b/(a+b))*density of H2O.

The logic they used in the explanation is that since a<b, the density of Z is less that H2O. Later they say, since b>a, Z is more than 1/2 the density of water. How did they come to these conclusions based on the heights of a and b?

Also, how would the problem change if a>b?

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