Pointing to the lady on the platform, Manju said, "She is the sister of the father of my mother's son." How is the lady related to Manju?

Introduction / Context:
This problem uses the phrase my mother's son, which is a common way to indirectly refer to oneself or to a brother, and then talks about the father of that person and the sister of that father. You must decode whose father is being referred to, then reach his sister, and finally see how that lady is related to Manju.

Given Data / Assumptions:
- Speaker: Manju. - The lady is described as the sister of the father of my mother's son. - My mother's son could be Manju herself (if Manju is male) or Manju's brother (if Manju is female). - The father of my mother's son is Manju's father. - The lady is the sister of Manju's father.

Concept / Approach:
The core is to understand that my mother's son refers to a child of the same parents as the speaker. The father of this child is simply the speaker's father. The lady is then the sister of this father, which is a classic definition of a paternal aunt. Therefore, from Manju's perspective, the lady is her aunt. The gender of Manju is not crucial; the relationship through the parents remains the same.

Step-by-Step Solution:
Step 1: Interpret my mother's son. This phrase means a male child of Manju's mother. That could be Manju himself (if Manju is male) or Manju's brother (if she is female), but in either case, the child shares the same mother as Manju. Step 2: The father of my mother's son is the husband of Manju's mother, that is, Manju's father. Step 3: The lady on the platform is described as the sister of this father, making her the sister of Manju's father. Step 4: The sister of one's father is one's paternal aunt. Step 5: Therefore, from Manju's perspective, the lady is her aunt.

Verification / Alternative check:
Imagine a small family: Manju's parents (father and mother) at one level and their children (including Manju) at the next. The phrase my mother's son points to one of those children. The father of that son is the same father for all those children. Now add the lady as a sister of that father. In a normal family tree, that person is always an aunt to the children of her brother. This confirms the answer.

Why Other Options Are Wrong:
- Mother: Manju's mother is the wife of his father, not the sister of his father. - Sister: A sister of Manju would share the same parents and belong to the same generation, not be a sibling of Manju's father. - Niece: A niece would be the daughter of Manju or of Manju's sibling, a generation below Manju, not above. - Grandmother: A grandmother is the mother of a parent, not the sister of a parent. Here the lady is explicitly called a sister of Manju's father, not his mother.

Common Pitfalls:
Some learners mistakenly read my mother's son as my mother's brother and then lose track of generations. Another pitfall is thinking that the sister of the father of my mother's son is somehow the mother's sister, which is not correct in the given wording. Always convert complex phrases like my mother's son into simpler, familiar relations such as my brother or myself.

Final Answer:
The lady is Manju's aunt.