Explanation

(c) $\frac{1}{\lambda} = R\left( \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right)$
For first line of Lyman series $n_{1} = 1$ and $n_{2} = 2$
For first line of Balmer series $n_{2} = 2$ and $n_{2} = 3$
So, $\frac{\lambda_{Lyman}}{\lambda_{Balmer}} = \frac{5}{27}$