Question

Two miscible fluids of densities $1.2gm/c{m}^3$ and $1.4gm/c{m}^3$ 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

Density of liquid $1,{\rho }_1=1.2gm/c{m}^3$
Density of liquid $2,{\rho }_2=1.4gm/c{m}^3$
Let us say that the first liquid mixed has a volume = 3v and second liquid mixed has a volume = 5v
Such that the ratio proportion $=\frac{3v}{5v}=\frac{3}{5}$ (As given)
From the above we can say that liquid 1 has mass $={\rho }_1\times 3v$ and liquid 2 has mass $={\rho }_2\times 5v$ in the mixture.
From definition,
$\rho =\frac{m_1+m_2}{v_1+v_2}i.e.,\frac{Totalmass}{Totalvolume}$
$\Rightarrow \rho$ of resulting mixture $=\frac{3{\rho }_{1}v+5{\rho }_{2}v}{3v+5v}$
$=\frac{(1.2\times 3)+(1.4\times 5)}{8}=1.325\frac{gm}{c{m}^3}$