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Two substances of densities $ρ_{1} a n d ρ_{2}$ are mixed in equal volumes. The density of mixture is 4 units. When they are mixed in equal masses the density of the mixture is 3 units. The value of $ρ_{1} a n d ρ_{2}$ are ___ units

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12, 4

6, 2

10, 12

3, 5

answer is A.

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Detailed Solution

$4 = \frac{ρ_{1} + ρ_{2}}{2} \Rightarrow ρ_{1} + ρ_{2} = 8 \to (1) 3 = \frac{2 ρ_{1} ρ_{2}}{ρ_{1} + ρ_{2}} \Rightarrow ρ_{1} ρ_{2} = 12 \to (2) \Rightarrow ρ_{1} = 6, ρ_{2} = 2$

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