For Lyman series
${\mathrm{\nu }}_{\text{Lymen}}=\frac{\mathrm{c}}{{\mathrm{\lambda }}_{\max }}=\mathrm{Rc}\left[\frac{1}{{\left(1\right)}^2}-\frac{1}{{\left(2\right)}^2}\right]=\frac{3\mathrm{RC}}{4}$
For Balmer series
${\mathrm{\nu }}_{\text{Balmer}}=\frac{\mathrm{c}}{{\mathrm{\lambda }}_{\max }}=\mathrm{Rc}\left[\frac{1}{{\left(2\right)}^2}-\frac{1}{{\left(3\right)}^2}\right]=\frac{5\mathrm{RC}}{36}$
$\therefore \frac{{\mathrm{\nu }}_{\text{Lymen}}}{{\mathrm{\nu }}_{\text{Balmer}}}=\frac{27}{5}$