A body floats with 1/3 ^rd of its volume outside water and in other case same body floats with  3/4 ^th of its volume inside another liquid. The density of the liquid is

Let V be the volume of the body. Then the volume immersed in water is $\frac{2}{3}V$ and that
immersed in the liquid is $\frac{3}{4}\mathrm{V}$ .

Let ${\rho }_l$ be the density of the liquid. 

The density of water is ${\mathrm{\rho }}_{\mathrm{w}}=1\mathrm{g}/{\mathrm{cm}}^3$ 

Weight of body $=\frac{2}{3}{\mathrm{V\rho }}_{\mathrm{w}}\mathrm{g}+\frac{3}{4}{\mathrm{V\rho }}_{\mathrm{l}}\mathrm{g}$

$\Rightarrow {\mathrm{\rho }}_{\mathrm{l}}=\frac{8}{9}{\mathrm{\rho }}_{\mathrm{w}}=\frac{8}{9}\mathrm{g}/{\mathrm{cm}}^3$