According to Bohr, the wavelength emitted when an electron jumps from ${n_1}^{th}$ to ${n_2}^{th}$ orbit is

$E = \frac{hc}{\lambda } = E_2 –E_1$

$\frac{1}{\lambda }$ $= R$ $\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$

For first-line in Lyman series

$\frac{1}{{\lambda }_L}$ $=R\left(\frac{1}{1^2}-\frac{1}{2^2}\right)$ = $\frac{3 R}{4}$ ...(i)

For first-line in Balmer series,

$\frac{1}{{\lambda }_B}$ $=R\left(\frac{1}{2^2}-\frac{1}{3^2}\right)$ = $\frac{5 R}{36}$ ...(ii)

From Eqs. (i) and (ii)

$\therefore \frac{{\lambda }_B}{{\lambda }_L}$ $=\frac{3 R}{4}\times \frac{36}{5R}$ $=$ $\frac{27}{5}$

$\therefore {\lambda }_B=$$\frac{27}{5}\lambda (\because {\lambda }_L=\lambda )$