Population $A$: $101, 102, \ldots, 200$
Population $B$: $151, 152, \ldots, 250$
Using Property:
Variance is independent of change of origin
i.e., if each observation is increased or decreased by a constant, variance remains unchanged
Here, each observation of $B$ = each observation of $A$ $+ 50$
$\Rightarrow$ Population $B$ is obtained by adding $50$ to each observation of population $A$
$\Rightarrow V_B = V_A$
$\therefore \dfrac{V_A}{V_B} = \boxed{1}$