A piece of granite floats at the interface of mercury and water contained in a beaker as in figure. If the densities of granite, water and mercury are $ρ, ρ_{1}$ and $ρ_{2}$ respectively, the ratio of the volume of granite in water to the volume of granite in mercury is

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​ V 1 ​ ρ 1 ​ g + V 2 ​ ρ 2 ​ g = V ρ g ⇒ V 1 ​ ρ 1 ​ g + V 2 ​ ρ 2 ​ g = ( V 1 ​ + V 2 ​ ) ρ g ⇒ V 1 ​ ρ 1 ​ g − V 1 ​ ρ g = V 2 ​ ρ g − V 2 ​ ρ 2 ​ g , ⇒ V 1 ​ ( ρ − ρ 1 ​ ) = V 2 ​ ( ρ 2 ​ − ρ ) ⇒ V 2 ​ V 1 ​ ​ = ρ − ρ 1 ​ ρ 2 − ​ ρ ​ ​

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