The percentage composition of carbon by mole in methane is:

First, recall the definition of mole (or atomic) percentage of an element in a compound. The formula is stated as

$$\text{Mole \% of an element} \;=\; \frac{\text{Number of moles (or atoms) of that element in one mole of the compound}}{\text{Total number of moles (or atoms) of all elements in one mole of the compound}} \times 100\%.$$

We have methane, whose molecular formula is $$\mathrm{CH_4}.$$ This means that in one molecule (or equivalently, in one mole) of methane there are

$$1 \text{ atom of carbon}$$ and $$4 \text{ atoms of hydrogen}.$$

Now, let us find the total number of atoms present in one molecule of methane:

Total atoms $$\;=\; 1 \;($$ from carbon $$) \;+\; 4 \;($$ from hydrogen $$) \;=\; 5.$$

So, the number of carbon atoms is $$1,$$ and the total number of atoms is $$5.$$ Substituting these numbers into the mole-percentage formula, we get

$$\text{Mole \% of C in CH}_4 \;=\; \frac{1}{5}\times100\%.$$

Simplifying,

$$\frac{1}{5}\times100\% \;=\; 20\%.$$

Hence, the correct answer is Option B.