To answer this question, we need to analyze the statements made by the sister and the brother.
The sister claimed that she is older, while the brother claimed that he is younger.
If the sister is telling the truth, then the brother must be lying because their statements contradict each other.
If the brother is telling the truth, then the sister must be lying because their statements contradict each other.
Since we know that at least one of them is lying, it is not possible for both of them to be telling the truth.
Therefore, the brother is older and the correct answer is option B.