Same mass of ${\mathrm{CH}}_4\text{ and }{\mathrm{H}}_2$ is taken in container. The partial 

pressure caused by ${\mathrm{H}}_2$ is

$N_{{\mathrm{CH}}_4}=\text{ number of moles of }{\mathrm{CH}}_4=\frac{m}{16}$

$N_{H_2}=\text{ number of moles of }{H}_2=\frac{m}{2}$

fraction partial pressure of ${\mathrm{H}}_2$ is

$H_2=\frac{n_{H_2}}{n_{H_2}+n_{C{H}_4}}=\frac{\frac{m}{2}}{\frac{m}{2}+\frac{m}{16}}=\frac{\frac{m}{2}}{9m}=\frac{8}{9}$