One should be careful about ____ duty. ?

The phrase "One should be careful about ____ duty" requires a possessive pronoun to indicate whose duty is being referenced. Among the options provided, 'one's' is the most suitable because it directly correlates with the indefinite pronoun 'one' used at the start of the sentence.

'One’ is used to refer to a person in a general sense, and ‘one’s’ serves as the possessive form of ‘one.’ Therefore, saying "One should be careful about one’s duty" effectively conveys that each individual has personal responsibilities to be cautious about.

Let's examine the other options. 'His' (A) could imply a male individual, which restricts the interpretation and does not align with the neutral reference 'one.' 'The duty' (C) lacks a possessive context, making the sentence awkward and ambiguous regarding whose duty is in question. Finally, 'other’s' (D) suggests belonging to someone else, which detracts from the intended meaning of self-awareness regarding one's responsibilities.

Thus, 'one’s' is the correct choice as it maintains consistency in tone and clarity in conveying the idea of personal responsibility.