Prove that in communicating vessels the height of the pillars above the interface

Prove that in communicating vessels the height of the pillars above the interface of two dissimilar liquids is inversely proportional to the densities of the liquids.

We use the formula to calculate the fluid pressure:

P = pgh

Water pressure: Рв = рв • g * hв.

Kerosene pressure: Pker = pker • g * hker Let us express the height of the liquid from both formulas:

hker = Rker / (Rker * g)

Find the height ratio:
hv / hker = (Pw * Rker * g) / (Pker * rvody * g)
It can be seen from this ratio that the heights of the pillars below the interface level of two dissimilar liquids are inversely proportional to the densities of the liquids.

That is, the lower the density, the higher the column, and vice versa.