Question

Two substances of densities ${\rho }_1$ and ${\rho }_2$ are mixed in equal volume and the relative density of mixture is $4$. When they are mixed in equal masses, the relative density of the mixture is $3$. The values of ${\rho }_1$ and ${\rho }_2$ are :

• A. ${\rho }_1=6$ and ${\rho }_2=2$
• B. ${\rho }_1=3$ and ${\rho }_2=5$
• C. ${\rho }_1=12$ and ${\rho }_2=4$
• D. None of these

Answer 1

The correct option is A ${\rho }_1=6$ and ${\rho }_2=2$

When substances are mixed in equal volume then density $=\frac{{\rho }_1+{\rho }_2}{2}=4$

$\Rightarrow {\rho }_1+{\rho }_2=\mathrm{8...}\left(i\right)$

when substances are mixed in equal masses then density

$\frac{2{\rho }_1{\rho }_2}{{\rho }_1+{\rho }_2}=3$

$2{\rho }_1{\rho }_2=3({\rho }_1+{\rho }_2)...\left(ii\right)$

On solving (i) and (ii) we get

${\rho }_1=6;{\rho }_2=2$