If two liquids are mixed in equal volumes, their resultant density is $\text{5}\text{gr/cc}$ and mixed in equal masses their resultant density is$4.8\text{g/cc}$ . The ratio of their densities is$\frac{2}{\text{k}}$ . Then k is

$\frac{2{\rho }_1{\rho }_2}{{\rho }_1+{\rho }_2}=4.8\Rightarrow {\rho }_1{\rho }_2=24\to \left(2\right)$

${\left({\rho }_1-{\rho }_2\right)}^2={\left({\rho }_1+{\rho }_2\right)}^2-4{\rho }_1{\rho }_2$

$=100-4\times 24=4$

${\rho }_1-{\rho }_2=\pm 2\to \left(3\right)$

Add equations (1) and (3)

$2{\rho }_1=12\Rightarrow {\rho }_1=6\text{g/cc}$

$\text{6}+{\rho }_2=10\Rightarrow {\rho }_2=4\text{g/cc}$

$\frac{{\rho }_1}{{\rho }_2}=\frac{6}{4}=\frac{3}{2}$

${\rho }_1+{\rho }_2=10$

$\underset{\_}{{\rho }_1-{\rho }_2=-2}$

$2{\rho }_1=8\Rightarrow {\rho }_1=4\text{g/c}\text{.c}$

${\rho }_2=6\text{g/c}\text{.c}$

$\frac{{\rho }_1}{{\rho }_2}=\frac{4}{6}=\frac{2}{3}=\frac{2}{\text{K}}$

$\Rightarrow \text{K}=3$