Two non-reactive monoatomic ideal gases have their atomic masses in...

Given, $\dfrac{{\text{m}}_{\text{A}}}{{\text{m}}_{\text{B}}} = \dfrac{2}{3 }$
$∵$ Volume and temperature is same.
From ideal gas equation, $PV = nRT$
$\dfrac{\text{P}}{\text{n}} = constant$
$\dfrac{{\text{P}}_{\text{A}}}{{\text{n}}_{\text{A}}} = \dfrac{{\text{P}}_{\text{B}}}{{\text{n}}_{\text{B}}} ⇒ \dfrac{{\text{n}}_{\text{A}}}{{\text{n}}_{\text{B}}} = \dfrac{{\text{P}}_{\text{A}}}{{\text{P}}_{\text{B}}} = \dfrac{4}{3}$

Also, density, $ρ = \dfrac{M}{V}$
$\dfrac{{\text{ρ}}_{\text{A}}}{{\text{ρ}}_{\text{B}}} = \dfrac{{\text{M}}_{\text{A}} / \text{v}}{{\text{M}}_{\text{B}} / \text{v}} = \dfrac{{\text{n}}_{\text{A}} {m}_{\text{A}}}{{\text{n}}_{\text{B}} {\text{m}}_{\text{B}}}$
$= \dfrac{4}{3} \times \dfrac{2}{3} = \dfrac{8}{9}$.