Question

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

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

Answer 1

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

Density $=\frac{\text{Total mass}}{\text{Total volume}}$
${\rho }_{mix}=\frac{m+m+m}{v_1+v_2+v_3}$
$=\frac{3m}{V_1+V_2+V_3}=\frac{3m}{\frac{m}{d}+\frac{m}{2d}+\frac{m}{3d}}$ $\because (Volume=\frac{\text{mass}}{\text{density}})$
${\rho }_{mix}=\frac{3\times 6}{11}d=\frac{18}{11}d$