If ${\lambda }_1$ and ${\lambda }_2$ are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of ${\lambda }_1:{\lambda }_2$ is 

The wavelength of spectral line of the third member of Lyman series is given by $\frac{1}{{\lambda }_1}=R\left[\frac{1}{1}-\frac{1}{16}\right]\Rightarrow {\lambda }_1=\frac{16}{15R}$ …………. (i)

The wavelength of spectral line of the first member of paschen series is given by $\frac{1}{{\lambda }_2}=R\left[\frac{1}{9}-\frac{1}{16}\right]\Rightarrow {\lambda }_2=\frac{144}{7R}$    …………. (ii)

Dividing (ii) by (i) we get $\frac{{\lambda }_1}{{\lambda }_2}=\frac{16}{15R}\times \frac{7R}{144}=\frac{7}{135}$