Maximum number of atoms in the ground state
Of the $100$, initially some are in $n=1$, and some in $n=2$ and then some in $n=5$ after absorbing 155 nm then some in lots of other levels after photons emitted. Thus, eventually, none will be left in $n = 5$ but spread  in all in the other levels  including the ground state. However, all other possible transitions occur ($n=2 \to 1$ for example) so all end up in the ground state in total $(100-b)$. However, you do not know the initial amount $b$ so I'm not sure that this question can be answered except that the ratio is $b/(100-b)$.