Question

Equal masses of two liquids having densities $d_1$ and $d_2$ are mixed together. The density of the resulting mixture is

• A. $\frac{d_1+d_2}{2}$
• B. $\frac{d_1-d_2}{d_1{d}_2}$
• C. $\frac{d_1{d}_2}{d_1+d_2}$
• D. $\frac{2d_1{d}_2}{d_1+d_2}$

Answer 1

The correct option is D $\frac{2d_1{d}_2}{d_1+d_2}$

Let the mass of each liquid be $M$ and densities are $d_1$ and $d_2$ respectively.
$\text{Volume}=\frac{\text{Mass}}{\text{Density}}$
$\Rightarrow d_{\text{mix}}=\frac{M_{\text{mix}}}{V_{\text{mix}}}=\frac{M+M}{\left(\frac{M}{d_1}\right)+\left(\frac{M}{d_2}\right)}$
$\therefore d_{\text{mix}}=\frac{2d_1{d}_2}{d_1+d_2}$