Ratio of the wavelengths of first line of Lyman series and first line of Balmer series is

$\frac{1}{\mathrm{\lambda }}=\mathrm{R}\left(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right)$
For first line of Lymen series n₁ = 1 and n₂ = 2
For first line of Balmer series n₂ = 2 and n₂ = 3
So, $\frac{{\mathrm{\lambda }}_{\mathrm{Lymen}}}{{\mathrm{\lambda }}_{\mathrm{Balmer}}}=\frac{5}{27}$