Question

Three liquids of densities $d,2d$ and $3d$ are mixed in equal proportions of weights. What is the relative density of the mixture, if $d$ is the density of water?

• A. $\frac{11}{7}$
• B. $\frac{18}{11}$
• C. $\frac{13}{9}$
• D. $\frac{23}{18}$

Answer 1

The correct option is B $\frac{18}{11}$

The three liquids of densities $d,2d$ & $3d$ are mixed in equal proportions of weights. Let $m$ be the mass of each liquid.
$\therefore {\rho }_{\text{mixture}}=\frac{3m}{V_1+V_2+V_3}=\frac{3m}{\frac{m}{d}+\frac{m}{2d}+\frac{m}{3d}}$
$\Rightarrow {\rho }_{\text{mixture}}=\frac{3\times 6}{11}d=\frac{18}{11}d$
$\Rightarrow \frac{{\rho }_{\text{mixture}}}{d}=\frac{18}{11}$
As, $d$ is density of water, so, relative density of mixture $=\frac{18}{11}$.