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Directions: There are six persons P, Q, R, S, T and U in a family. R is the sister of U. Q is the brother of T's husband. S is the father of P and the grandfather of U. There are exactly two fathers, three brothers and one mother in the group. Who is the mother?

Difficulty: Hard

Correct Answer: T

Explanation:


Introduction / Context:

This is a multi-step family-relation puzzle involving six people and role counts such as "two fathers" and "three brothers". These problems are common in banking and SSC exams because they test whether you can integrate explicit relationships with numerical constraints on family roles, without contradicting any clue.


Given Data / Assumptions:

  • Members: P, Q, R, S, T and U.
  • R is the sister of U.
  • Q is the brother of T's husband.
  • S is the father of P and the grandfather of U.
  • There are exactly two fathers, three brothers and one mother in the group.
  • We assume a single simple family with standard meanings of father, mother, brother, sister and husband.


Concept / Approach:

We first use the direct parent–child relationships to determine generations: grandparents, parents and children. Then we assign genders and marital links consistent with the clues. Finally, we check the counts: exactly two people must be fathers, exactly three must be in the role of brothers, and there must be exactly one mother. Any arrangement that violates these counts must be rejected, and the arrangement that works will reveal who the mother is.


Step-by-Step Solution:

Step 1: S is the father of P and the grandfather of U. So S is male and in the oldest generation. Since S is U's grandfather through P, P must be a parent of U. Step 2: R is the sister of U, so R and U are siblings and children of P. Since R is specifically called a sister, R is female. Step 3: Because S is already one father, and there must be exactly two fathers, P must be the second father. So P is male and is the father of R and U. Step 4: Q is the brother of T's husband. If T is married, her husband can naturally be P. Then Q is P's brother. That makes Q male and a brother to P. Step 5: With Q as P's brother and P as Q's brother, we now have two males who are brothers. If U is taken as male (brother of R), then Q, P and U together form the three "brothers" required by the problem. Step 6: There must be exactly one mother. R is a sister in the children's generation, and T is the only remaining candidate to be the mother. As the wife of P, T becomes the mother of R and U. Step 7: Check role counts: fathers = S and P (two fathers); brothers = P, Q and U (three brothers); mother = T (one mother). All constraints are satisfied, so this configuration is consistent.


Verification / Alternative check:

Try to make any other person the mother. If R were the mother, she could not also be described as U's sister. If Q were the mother, it would contradict the fact that Q is a brother. Making S the mother contradicts "S is the father of P". Therefore, the only consistent choice is T as the mother, with T married to P.


Why Other Options Are Wrong:

S is explicitly stated to be a father, not a mother.

Q is clearly male and a brother of T's husband, so Q cannot be the lone mother.

R is in the children's generation as the sister of U, not the parent of U.


Common Pitfalls:

Candidates often ignore the numerical constraints and stop as soon as they find any arrangement that fits some of the relations. However, all conditions must be satisfied simultaneously: two fathers, three brothers and exactly one mother. Always verify the counts after building a tentative family tree, and adjust assumptions about gender (like U's gender) only in ways that respect every clue.


Final Answer:

The mother in the group is T.

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