(x)/(x + 4) is the ratio of energies of photons produced due to...

Energy of a photon released in transition of electron in hydrogen atom is given by,

$E = 13 . 6\left(\dfrac{1}{{{n}_{2}}^{2}} - \dfrac{1}{{{n}_{1}}^{2}}\right)eV$

$⇒ \dfrac{{E}_{1}}{{E}_{2}} = \dfrac{13 . 6\left(\dfrac{1}{4} - \dfrac{1}{9}\right)}{13 . 6\left(\dfrac{1}{4} - \dfrac{1}{\infty}\right)} = \dfrac{x}{x + 4} ⇒ \dfrac{\dfrac{1}{4} - \dfrac{1}{9}}{\dfrac{1}{4}} = \dfrac{x}{x + 4}$

$⇒ \dfrac{5}{9} = \dfrac{x}{x + 4}$

$⇒ 5x + 20 = 9x$

$⇒ x = 5$