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