Option C: The words 'young, old and ______' refer to individuals belonging to different age groups. Hence the word that also belongs to an age group is 'children'.
There must be some cohesion between the words, to bring out a unified meaning.
Hence option C 'children' is correct.
Options A, B and D: 'Woman' and 'men' refer to gender groups, and do not indicate age.
'Modern' refers to the recent times, and not any age groups.
Hence these words do not complete the sentence in meaning.
So, options A, B and D are incorrect.