To determine the missing number 'X' in the series 7, X, 21, 31, 43, let's analyze the differences between consecutive terms:

• 21 - 31 = $10$
• 31 - 43 = $12$

The differences between 31 and 21, and between 43 and 31, are increasing by 2 (10 and 12).

Following this pattern, the difference between X and 21 should be 8.

Therefore, X = 21 - 8 = $13$.

Thus, the missing number 'X' is 13.

The correct option is C.