Two miscible fluids of densities 1.2 gm/cm³ and 1.4 gm/cm³ are mixed with a proportion of their volumes equal to 3:5. Assuming both fluids to be perfectly miscible, what is the density of resulting liquid?

0.325 gm/cm³

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1.325 gm/cm³

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1.3 gm/cm³

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2.425 gm/cm³

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Solution

The correct option is B
1.325 gm/cm³

Given,
Density of liquid 1 = ρ₁=1.2 gm/cm³
Density of liquid 2 = ρ₂= 1.4 gm/cm³
Let us say that the first liquid mixed has a volume= $3 v$ and second liquid mixed has a volume= $5 v$
Such that the ratio remains same
i.e $\frac{3 v}{5 v} = \frac{3}{5}$
From above we can say that liquid 1 has mass = ρ₁ $\times 3 v$ and liquid 2 has mass = ρ₂ $\times 5 v$ in the mixture
From definition,
$ρ = \frac{m_{1} + m_{2}}{v_{1} + v_{2}}$

i.e., $\frac{total mass}{total volume}$

⇒ ρ of resulting mixture = $\frac{3 ρ_{1} v + 5 ρ_{2} v}{3 v + 5 v}$
$= \frac{(1.2 \times 3) + (1.4 \times 5)}{8}$
$= 1.325$ $g / c m^{3}$

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Two miscible fluids of densities 1.2 gm/cm3 and 1.4 gm/cm3 are mixed with a proportion of their volumes equal to 3:5. Assuming both fluids to be perfectly miscible, what is the density of resulting liquid?

Two miscible fluids of densities 1.2 gm/cm³ and 1.4 gm/cm³ are mixed with a proportion of their volumes equal to 3:5. Assuming both fluids to be perfectly miscible, what is the density of resulting liquid?