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

Answer: (A)

When substances are mixed in equal volume then density
$=\frac{{\rho }_1+{\rho }_2}{2}=4$
$\Rightarrow \frac{{\rho }_1+{\rho }_2}{2}=4$
$\Rightarrow {\rho }_1+{\rho }_2=8$...(i)
When substances are mixed in equal masses then density
$=\frac{2{\rho }_1{\rho }_2}{{\rho }_1+{\rho }_2}=3$
$\Rightarrow 2{\rho }_1{\rho }_2=3\left({\rho }_1+{\rho }_2\right)$ ...(ii)
On solving (i) and (ii) we get
${\rho }_1=6$ and ${\rho }_2=2$.