Question

When equal volumes of two liquids are mixed, the specific gravity of the mixture is 4. When equal masses of the same two liquids are mixed the specific gravity of the mixture is 3. Find specific gravities of two liquids.

Answer 1

Let ${\rho }_1$ and ${\rho }_2$ be the densities of two liquids.

when equal volume of two liquids are mixed , then specific gravity ($\rho$) is given by $\rho$ = $\frac{({\rho }_1+{\rho }_2)}{2}$

and when equal masses of two liquids are added ,then specific gravity ($\rho$) = 2($\frac{{\rho }_1{\rho }_2}{{\rho }_1+{\rho }_2}$)

so we have $\frac{{\rho }_1+{\rho }_2}{2}$ = 4 ....................(1)

and 2($\frac{{\rho }_1\times {\rho }_2}{{\rho }_1+{\rho }_2}$) = 3 ..........(2)

on solving 1st and 2nd we get ${\rho }_1=6$ and ${\rho }_2=2$