The density of water at the surface of ocean is $\rho$. If the bulk modulus of water is B, then the density of ocean water at depth, when the pressure is $\alpha p_0$ where $p_0$ is the atmospheric pressure, is

From the definition of bulk modulus

As we move from surface to place where pressure changes to $\alpha p_0$, let us assume volume changes by $\mathrm{\Delta }$V, then

$B=\frac{V\mathrm{\Delta }p}{\mathrm{\Delta }V}=\frac{V(\alpha -1)p_0}{\mathrm{\Delta }V}$

$\text{ New volume, }V\text{'}=V-\mathrm{\Delta }V=V\left[1-\frac{(\alpha -1)p_0}{B}\right]$

$\text{ Density at the given depth, }\rho \text{'}=\rho \frac{V}{V\text{'}},\text{ where }\rho \text{ is density at surface}$

$\Rightarrow \rho \text{'}=\frac{\rho \times B}{B-(\alpha -1)p_0}$