In a family of six persons—Abhay, Banta, Cathy, Deepak, Emily and Fatima,…

Concept: In a family / blood-relation puzzle, first use every explicit gender clue (“wife of”, “husband of”, “mother-in-law of”, “sister of”, “father of”) to fix who is male and who is female, then use the marriage and parent-child clues to attach each person to one of the family's married couples. Once the family tree is fixed this way, any “How is X related to Y” question is read straight off the tree.

Working it out: Apply that method to the clues in order:

1. Abhay is called “the wife of Cathy”, so Abhay is female and Cathy is male.

2. Emily is “the mother-in-law of Abhay” — the mother of Abhay's husband — so Emily is Cathy's mother, and Emily is female.

3. “Deepak is the father of Fatima” and “Banta … is the sister of Fatima”, so Deepak, Banta and Fatima form one father-and-children set, with Banta female.

4. These clues fix three females this way — Abhay, Banta and Emily. Since the family has exactly three males and three females, the other three members, Cathy, Deepak and Fatima, must all be male.

5. Emily is Cathy's mother (step 2), and Deepak is the father of Fatima and Banta (step 3). With only two married couples in the family, and Abhay–Cathy already one couple, Deepak and Emily must be the second couple — the joint parents of Cathy, Banta and Fatima — leaving Banta and Fatima as the family's two unmarried members.

6. Since Fatima is male (step 4) and Emily is Fatima's mother (step 5), Fatima is Emily's son.

Cross-check: Each other option needs a different family map to hold, and none of them does:

• “Brother” would need Fatima to sit in Emily's own generation, but step 5 places Fatima a generation below Emily, as her child, not her sibling.

• “Father” would need the parent-child direction to run from Fatima to Emily, but the clue “Deepak is the father of Fatima” and the couple link in step 5 both run the opposite way — Emily is the parent, Fatima the child.

• “Daughter” would need Fatima to be female, but step 4 already fixes Fatima as one of the family's three males from the gender count.

Independent check: The same family map also resolves every person's cold drink consistently, which confirms the tree above is the only one that fits all the clues:

(Deepak dislikes Thums Up and Pepsi, so he takes the only drink left, Fanta; Cathy dislikes Pepsi, so he takes Thums Up; Abhay is then left with Pepsi.)