Arun says, "This girl is the wife of the grandson of my mother." In this blood relation question, who is Arun with respect to the girl?

Introduction / Context:
In this problem, Arun describes a girl as the wife of the grandson of his mother. We must figure out Arun's relation to that girl. The phrase "grandson of my mother" can refer to several people in principle, but the standard reasoning approach focuses on the most direct interpretation, which is very often Arun's own son.

Given Data / Assumptions:
• Arun refers to his own mother.• The grandson of Arun's mother is a male in the next generation.• This grandson can be Arun's son or the son of one of Arun's siblings.• The girl is the wife of this grandson.• Standard exam interpretation usually takes the grandson here to be Arun's son unless otherwise indicated.

Concept / Approach:
If we treat the grandson of Arun's mother as Arun's own son, then the girl is the wife of Arun's son. A woman who is married to one's son is one's daughter in law. From the girl's perspective, Arun is her father in law. Other interpretations, such as the grandson being a nephew of Arun, are possible in theory but are not usually taken as the intended reading in classical reasoning questions of this form.

Step-by-Step Solution:
Step 1: Let M be Arun's mother.Step 2: The grandson of M is any male child of M's children.Step 3: The most direct candidate for this grandson is Arun's own son.Step 4: Arun states that the girl is the wife of that grandson.Step 5: A girl who is married to a man's son is that man's daughter in law.Step 6: Therefore, from the girl's point of view, Arun is her father in law.

Verification / Alternative Check:
Visualize M at the top, with Arun as her son. Arun has a son who is M's grandson. The girl is married to this grandson, so she is the grandson's wife. Arun, as the father of that grandson, is the father in law of the girl. Even if M has other children with their own sons, the strongest and most common exam interpretation here remains that the grandson is Arun's son, preserving the neat father in law relationship.

Why Other Options Are Wrong:
Father of the girl: If Arun were her father, she would be described as the daughter of my mother's son rather than the wife of the grandson.Grandfather of the girl: A grandfather is the father of the girl's parent, not the father of her husband's parent.Husband of the girl: The husband of the girl is the grandson, not Arun.Uncle of the girl: An uncle would be the brother of her parent, which does not fit the description involving a grandson and his wife.

Common Pitfalls:
Some students misread the phrase grandson of my mother as my grandson and then either misplace Arun a generation higher or lower. Others assume the grandson must be the child of a sibling and thus treat Arun as an uncle in law. The cleanest interpretation in standard questions is to treat the grandson as Arun's son, leading to the father in law relation.

Final Answer:
Arun is the girl's father in law.