For hydrogen atom, λ _ 1 and λ _ 2 are the wavelengths...

Wavelength corresponding to the photon emitted in transition $n = 3ton = 1$ is

$\dfrac{1}{{\lambda}_{1}} = R\left(\dfrac{1}{{1}^{2}} - \dfrac{1}{{3}^{2}}\right) = \dfrac{8R}{9}$ ....(1)

Wavelength corresponding to the photon emitted for transition in transition $n = 2ton = 1$ is

$\dfrac{1}{{\lambda}_{2}} = R\left(\dfrac{1}{{1}^{2}} - \dfrac{1}{{2}^{2}}\right) = \dfrac{3R}{4}$ ....(2)

$\dfrac{{\lambda}_{1}}{{\lambda}_{2}} = \dfrac{3R}{4} \times \dfrac{9}{8R} = \dfrac{27}{32}$

Hence, the value of $x = 27$.