In the spectrum of hydrogen atom, the ratio of the longest wavelength in Lyman series to the longest wavelength in the Balmer series is

5/27 1/93 4/9 3/2

5/27

In Lyman series $\lambda_{\max }=\frac{4}{3 R}$ In Balmer series $\lambda_{\max }=\frac{36}{5 R}$. So required ratio = $\frac{5}{27}$