The f,rst line in the Lyman series has wavelength $\mathrm{\lambda }$. The wavelength of the first line in Balmer series is

For first line in Lyman series ${\mathrm{\lambda }}_{{\mathrm{L}}_1}=\frac{4}{3\mathrm{R}}...$ (1) 
For first line in Balmer series ${\mathrm{\lambda }}_{{\mathrm{B}}_1}=\frac{36}{5\mathrm{R}}...$.. (2)
From equations (1) and (2)

$\frac{{\mathrm{\lambda }}_{{\mathrm{B}}_1}}{{\mathrm{\lambda }}_{{\mathrm{L}}_1}}=\frac{27}{5}\Rightarrow {\mathrm{\lambda }}_{{\mathrm{B}}_1}=\frac{27}{5}{\mathrm{\lambda }}_{{\mathrm{L}}_1}\Rightarrow {\mathrm{\lambda }}_{{\mathrm{B}}_1}=\frac{27}{5}\mathrm{\lambda }$