# The Sphere Floats And Sinks

There are two liquids $$A$$ and $$B$$ of densities $$X$$ and $$Y$$ respectively. The liquids do not mix and $$A$$ floats on $$B$$.

There is a sphere $$C$$ of density $$Z$$ which floats stably at the interface of liquids $$A$$ and $$B$$, such that half of its volume is in $$A$$, and the other half is in $$B$$.

Which of the following gives the correct relationship between $$X,Y$$ and $$Z?$$

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