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 $\rho_{2}=2$.