Question

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?

• A. 0.325 gm/cm³
• B. 1.325 gm/cm³
• C. 1.3 gm/cm³
• D. 2.425 gm/cm³

Answer 1

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's say that the first liquid has a volume = $v_1=3v$ and the second liquid has a volume = $v_2=5v$

From above we can say that

Liquid 1 has mass = $m_1={\rho }_1\times 3v$ and liquid 2 has mass = $m_2={\rho }_1\times 5v$ in the mixture.
From definition, the density of the resulting liquid is given by,

$\rho =\frac{Totalmass}{Totalvolume}=\frac{m_1+m_2}{v_1+v_2}$
⇒So, density of resulting mixture = $\rho =\frac{(1.2\times 3)+(1.4\times 5)}{8}$

= $\rho =1.325gm/c{m}^3$.