Question

Two liquids of densities $2.5gm/c{m}^3$ and $0.8gm/c{m}^3$ are taken in the ration of their masses as $2:3$, respectively. Find the average density of the liquid combination.

Answer 1

Let the liquid be $2m$ am and $3m$ gm respectively. therefore, the volume of the first liquid of density $2.5gm/c{m}^3$ is $V_1=\frac{2m}{2.5}c{m}^3$
That of the second liquid is $V_2=\frac{3m}{0.8}c{m}^3$
Total volume $V=V_1+V_2=\frac{2m}{2.5}+\frac{3m}{0.8c{m}^3}$
Total mass $=2m+3m=5m$gm
Therefore, the average density
${\rho }_{av}=\frac{5m}{V}=\frac{5m}{\frac{2m}{2.5}+\frac{3m}{0.8}}=\frac{5}{\frac{2}{2.5}+\frac{3}{0.8}}=\frac{}{}gm/c{m}^3=1.09gm/c{m}^3$.