Two liquids of densities $ρ_{1} and ρ_{2}$ having equal masses are mixed together. The density of mixture will be

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ρ = \frac{m_{1} + m_{2}}{v_{1} + v_{2}}

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

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

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

answer is B.

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Detailed Solution

ρ_{1} and ρ_{2}

are densities of two liquids having same mass

m_{1} = m_{2} = m

Density of mixture $ρ$

$ρ = \frac{Total mass}{Total volume} = \frac{m_{1} + m_{2}}{v_{1} + v_{2}}$

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

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