According to Dalton's law of partial pressures, the total pressure by a mixture of gases is equal to the sum of the partial pressures of each of the constituent gases. 

$$\begin{gathered} {\mathrm{P}}_{\mathrm{i}}={\mathrm{x}}_{\mathrm{i}}\mathrm{P} \\ {\mathrm{P}}_{\mathrm{i}}= \mathrm{partial} \mathrm{pressure} \mathrm{of} {\mathrm{i}}^{\mathrm{th}} \mathrm{component}. \\ {\mathrm{x}}_{\mathrm{i}}=\mathrm{mole} \mathrm{fraction} \mathrm{of} \mathrm{the} {\mathrm{i}}^{\mathrm{th}} \mathrm{component} \\ \mathrm{P} = \mathrm{total} \mathrm{pressure} \end{gathered}$$

Let ${\mathrm{W}}_{{\mathrm{H}}_2}=40 \mathrm{g}\Rightarrow {\mathrm{n}}_{{\mathrm{H}}_2}=\frac{40}{2}=20$

${\mathrm{W}}_{{\mathrm{O}}_2}=60 \mathrm{g}\Rightarrow {\mathrm{n}}_{{\mathrm{O}}_2}=\frac{60}{32}=\frac{15}{8}$

${\mathrm{P}}_{{\mathrm{H}}_2}=\left(\frac{20}{20+\frac{15}{8}}\right)\times 2.2$

$=\frac{20}{20+1.875}\times 2.2$

$=\frac{20}{21.875}\times 2.2$

$=2.0114$

$\simeq 2.01\mathrm{bar}$