$(a)\;4:1\qquad(b)\;6:1\qquad(c)\;8:1\qquad(d)\;2:1$

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Given

Molar ratio of He and $CH_4$ is 4:1

Partial pressure ratio of He and $CH_4$ is 16:4

$\large\frac{n_{He}}{n_{CH_4}} = \sqrt{\large\frac{M_{CH_4}}{M_{He}}}\times\large\frac{P_{He}}{P_{CH_4}}$

Since total pressure = 20 bar

$= \sqrt{\large\frac{16}{4}}\times\large\frac{16}{4}$

Since time of diffusion for both is same

= 8:1

The composition of mixture initially gone out for He and $CH_4$ is 8:1

Hence answer is (c)

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