How are the relative gas volumes collected in the two tubes related to the relative number of gas molecules in the tubes?

For gases, the general equation applicable would be:

PV=znRT
where
P is pressure
V is volume
z is the compressibility factor
n is the number of moles
R is the gas constant
T is the absolute temperature

For simplicity, it is always assumed that the gas is ideal if otherwise stated. In this case, z=1. Also, it has been proved through derivation that the mole% is equal to the volume% for ideal gases. Therefore, the relative volumes and the relative moles are just equal.