The first 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 ${\mathrm{\lambda }}_{{\mathrm{L}}_1}=\frac{4}{3 \mathrm{R}}$-------(i)

For first line in Balmer series ${\mathrm{\lambda }}_{{\mathrm{B}}_1}=\frac{36}{5 \mathrm{R}}$------(ii)

From equation (i) and (ii) 
$\frac{{\mathrm{\lambda }}_{{\mathrm{B}}_1}}{{\mathrm{\lambda }}_{{\mathrm{L}}_1}}=\frac{27}{5}\Rightarrow {\mathrm{\lambda }}_{{\mathrm{B}}_1}=\frac{27}{5}{\mathrm{\lambda }}_{{\mathrm{L}}_1}\Rightarrow {\mathrm{\lambda }}_{{\mathrm{B}}_1}=\frac{27}{5}\mathrm{\lambda }$