Explanation
In atmosphere which gas have high partial pressure?
Let the weight of methane and hydrogen added be x grams.
Then, moles of methane$$ = \dfrac{x}{{16}}$$
And, moles of hydrogen$$ = \dfrac{x}{2}$$
Now , we know that $$PV = nRT$$.(where P is pressure, n is the number of moles, V is the volume, T is the temperature, and R is the gas constant.)
In this case, V, R and T are constant. Hence,$$P\propto n$$$$ \Rightarrow {P_{Total}}= \dfrac{x}{{16}} + \dfrac{x}{2} = \dfrac{9}{{16}}x$$ $$ \to (1)$$
Also, $${P_{Hydrogen}}\propto \dfrac{x}{2}$$ $$ \to (2)$$
Now, dividing equation (2) by (1), we get fraction of total pressure exerted by hydrogen$$ = \dfrac{{\dfrac{x}{2}}}{{\dfrac{{9x}}{{16}}}} = \dfrac{8}{9}$$, which is the required answer.
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