Pointing to a lady, Arun said: “The son of her only brother is the brother of…

In blood-relation puzzles, two people are treated as full siblings only if they share both parents (the standard convention, unless a half/step relation is explicitly stated), and a person becomes someone's father-in-law or mother-in-law only by being a parent of that person's spouse. So a clue of the form “X's son/daughter is Y's sibling” really says: Y and X's child share the same parents — so X, being a parent of that child, is a parent of Y as well.

1. Let L be the lady, and let B be her only brother.

2. The statement says B's son is the brother of Arun's wife (call her W). So B's son and W are siblings.

3. Siblings share a parent, so B — the father of that son — is also the father of W.

4. Being the father of Arun's wife makes B exactly Arun's father-in-law.

5. Since L is B's sister, L is the sister of Arun's father-in-law.

Checking this back against the statement: if B is Arun's father-in-law, then B's son and Arun's wife (W) are both children of B, so they are indeed siblings — exactly matching the given clue. The relation is consistent.

Why the other relations do not fit:

• Mother's sister — makes the brother a maternal uncle, whose son would be a cousin, not the wife's sibling.

• Mother-in-law — her brother would be the wife's maternal uncle, whose son would be the wife's cousin, not the wife's brother.

• Grandmother — puts her brother a generation removed, whose son would be an unrelated-generation relative, not the wife's sibling.