Three liquids of densities d, 2d and 3d are mixed in equal volumes. Then the density of the mixture is

The correct option is 2d.

Let us find the density of the mixture step-by-step.

Let the volume of each of the three liquids mixed together be $V$, since they are mixed in equal volumes.
Let the densities of the three liquids be:
${\rho }_1=d$
${\rho }_2=2d$
${\rho }_3=3d$

The mass of a liquid is given by the formula:
$\text{Mass}=\text{Density}\times \text{Volume}$

Using this formula, we can calculate the individual mass of each liquid:
Mass of the first liquid: $m_1={\rho }_1\times V=dV$
Mass of the second liquid: $m_2={\rho }_2\times V=2dV$
Mass of the third liquid: $m_3={\rho }_3\times V=3dV$

The total mass of the mixture ($m_{\text{total}}$) is the sum of the masses of individual liquids:
$m_{\text{total}}=m_1+m_2+m_3$
$m_{\text{total}}=dV+2dV+3dV=6dV$

The total volume of the mixture ($V_{\text{total}}$) is the sum of the volumes of the three liquids:
$V_{\text{total}}=V+V+V=3V$

The density of the mixture (${\rho }_{\text{mix}}$) is defined as the total mass divided by the total volume:
${\rho }_{\text{mix}}=\frac{m_{\text{total}}}{V_{\text{total}}}$

Substituting the values of total mass and total volume:
${\rho }_{\text{mix}}=\frac{6dV}{3V}$
${\rho }_{\text{mix}}=2d$

Thus, the density of the mixture is 2d.