Two different liquids of densities $ρ_{1}, ρ_{2}$ are having same volume V. When they with each other are mixed then the effective density of the mixture is given by

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$ρ = \frac{ρ_{1} ρ_{2}}{ρ_{1} + ρ_{2}}$

$ρ = \frac{ρ_{1} + ρ_{2}}{3}$

$ρ = \frac{2 ρ_{1} ρ_{2}}{ρ_{1} + ρ_{2}}$

$ρ = \frac{ρ_{1} + ρ_{2}}{2}$

answer is B.

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Detailed Solution

Two different liquids of densities $ρ_{1}, ρ_{2}$ are having same volume V. When they with each other are mixed.

$\begin{array}{ll} ρ = \frac{total mass}{total volume} \\ ρ = \frac{M_{1} + M_{2}}{V_{1} + V_{2}} ∴ ρ = \frac{M}{V} \\ ρ = \frac{ρ_{1} V_{1} + ρ_{2} V_{2}}{V_{1} + V_{2}} M_{1} = ρ_{1} V_{1}, M_{2} = ρ_{2} V_{2} \\ ρ = \frac{ρ_{1} V + ρ_{2} V}{V + V} ∴ V_{1} = V_{2} = V \\ ρ = \frac{V (ρ_{1} + ρ_{2})}{2 V} \\ ρ = \frac{ρ_{1} + ρ_{2}}{2} \end{array}$