The first line in the Lyman series has wavelength λ. The wavelength of the first line in Balmer series is :

$\frac{27}{5} \lambda$

For first line in Lyman series $\lambda_{L_1}=\frac{4}{3 R}$    ...... (i)

For first line in Balmer series $\lambda_{B_1}=\frac{36}{5 R}$  ...... (ii)

From equation (i) and (ii)

$\frac{\lambda_{B_1}}{\lambda_{L_1}}=\frac{27}{5} \Rightarrow \lambda_{B_1}=\frac{27}{5} \lambda_{L_1} \Rightarrow \lambda_{B_1}=\frac{27}{5} \lambda$