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Quantitative Aptitude · Blood Relations

Blood Relations: Counting Persons and Gender Determination

Updated 1 October 2026

These questions give statements about a family and ask how many sons, daughters or members there are, or what the gender of a person is. Solve them by listing every person, fixing gender from words like father or sister, drawing a small tree, and counting only what the statements prove.

Understand Counting Persons and Gender Determination

A blood relations puzzle describes a family in words. You must turn those words into a clear picture. Two things matter most: who is in the family and what is each person's gender.

Some words fix gender. Father, brother, son, uncle, nephew, husband, grandfather are male. Mother, sister, daughter, aunt, niece, wife, grandmother are female. Words like cousin, parent, child, sibling, spouse, grandchild and friend do not fix gender. If a puzzle says 'A is B's cousin', you cannot tell if A is male or female unless another clue says so.

Counting questions usually follow a pattern: 'A has 3 sisters. Each sister has 2 brothers.' Here you must watch who is counted. A person is never their own sibling. A girl's brothers are all the boys in the family. A boy's brothers are all the other boys. This difference is where most counting errors come from.

Other questions ask for the minimum number of members. For example, a family with 2 fathers, 2 sons and 1 grandfather can be just 3 people if one man is both father and son. Always ask whether one person can play two roles. Merge roles only where they are logically compatible (same gender, different generations or relations). A person cannot be both father and son of the same person, and a male role cannot merge with a female role.

When you list family members, let B be the number of boys and G the number of girls among the children. Count the parents separately. They are not part of B and G.

If the data does not prove a gender or a number, the right answer is often 'cannot be determined'. Learn to spot this. Never guess a gender that the statements do not fix.

Key formulas to remember

Sibling count from a boy's view
Brothers of a boy = (Total boys − 1); Sisters of a boy = Total girls
A boy does not count himself. All girls in the family are his sisters.
Sibling count from a girl's view
Brothers of a girl = Total boys; Sisters of a girl = (Total girls − 1)
A girl does not count herself. All boys are her brothers.
Total children from two views
Total children = Brothers of a boy + Sisters of a boy + 1
Add 1 for the boy himself. Use the same idea for a girl's view.
Gender-fixing words
Male: father, son, brother, uncle, nephew, husband. Female: mother, daughter, sister, aunt, niece, wife
Cousin, parent, child, sibling, spouse and friend do not fix gender.
Role overlap rule
One person can hold two compatible roles, such as father and son
Use this when a question asks for the minimum number of members. Roles must not contradict each other.

How to solve Counting Persons and Gender Determination questions

Use this method for any counting or gender question. It stops you from counting a person twice or assuming a gender.

  1. 1Read the whole question once. Note what is asked: a count, a gender, or a relation.
  2. 2List every named person and mark the gender if the word fixes it (M, F or ?).
  3. 3Draw a small tree. Put parents on top, children below, a double line for married couples.
  4. 4Add each statement one at a time. Update gender marks as new clues appear.
  5. 5For counting, decide whose point of view the statement uses. Remove that person from their own sibling count.
  6. 6Check whether one person can fill two roles. For minimum members, merge roles wherever they are compatible.
  7. 7Total the family and check it against every statement.
  8. 8If gender or number is still not forced, choose 'cannot be determined' if it is an option.

Quickest way: Sibling-count shortcut for MCQs

When to use it: Use this when the question gives a family's children from one person's view and asks for a number or a gender-based count.

  1. Write B for boys and G for girls as unknowns.
  2. Turn each statement into a small equation using the keyFormulas: boy's brothers = B − 1, boy's sisters = G, girl's brothers = B, girl's sisters = G − 1.
  3. Solve for B and G. These are usually small numbers.
  4. Test each option against the equations. Eliminate options that break any statement.
  5. If an option says 'cannot be determined' and your equations give one fixed answer, reject it.
  6. Skip a long chain puzzle on first pass. Come back if time remains. A wrong answer costs 0.25 marks.

Common mistakes in Counting Persons and Gender Determination

  • Counting the person as their own brother or sister

    You read 'A has 3 brothers' and count all boys in the family, including A.

    Fix: If A is a boy, A has (total boys − 1) brothers. Always remove the speaker from their own sibling count.

  • Assuming gender for cousin, parent or spouse

    Students assume cousin means male or spouse means female.

    Fix: Mark such persons with '?' until another clue fixes gender. If no clue appears, the answer may be 'cannot be determined'.

  • Counting parents inside the boys and girls totals

    You add the father and mother to B and G, which are meant for the children only.

    Fix: Keep B and G for the children. Count parents separately and add them only when the question asks for total members.

  • Never merging roles in minimum-member questions

    You give each role to a new person, so your count is too high.

    Fix: Ask if one person can be both father and son, or both brother and uncle. Merge wherever the roles are compatible.

  • Mixing up a girl's and a boy's sibling counts

    The same sentence form works for both, so the −1 goes to the wrong group.

    Fix: Remove one from the speaker's own gender only. Boy: boys − 1. Girl: girls − 1.

Worked examples

Example 1

In a family, each boy has as many sisters as brothers, but each girl has twice as many brothers as sisters. How many boys and girls are there?
(A) 3 boys, 4 girls
(B) 4 boys, 3 girls
(C) 3 boys, 3 girls
(D) 2 boys, 3 girls

Show the solution
  1. Let boys = B and girls = G.
  2. A boy's brothers = B − 1 and his sisters = G. So B − 1 = G.
  3. A girl's brothers = B and her sisters = G − 1. So B = 2(G − 1).
  4. Put B = G + 1 into the second equation: G + 1 = 2G − 2, so G = 3.
  5. Then B = G + 1 = 4.
  6. Check: a boy has 3 brothers and 3 sisters. A girl has 4 brothers and 2 sisters, and 4 = 2 × 2.

Answer: (B) 4 boys, 3 girls

Example 2

A has 3 sisters and 2 brothers. A is a boy. How many children are there in the family, and how many girls?
(A) 6 children, 3 girls
(B) 5 children, 3 girls
(C) 6 children, 2 girls
(D) 5 children, 2 girls

Show the solution
  1. A is a boy, so his sisters = all girls. Girls = 3.
  2. His brothers = boys − 1 = 2, so boys = 3 (this includes A).
  3. Total children = boys + girls = 3 + 3 = 6.
  4. Check with the formula: brothers + sisters + 1 = 2 + 3 + 1 = 6.

Answer: (A) 6 children, 3 girls

Example 3

In a group there are 2 fathers, 2 sons and 1 grandfather. What is the minimum number of persons in the group?
(A) 5
(B) 4
(C) 3
(D) 2

Show the solution
  1. Roles can overlap, so look for the smallest chain.
  2. Take three men: grandfather G, his son S1, and S1's son S2.
  3. G is the grandfather and also a father (of S1). S1 is a father (of S2) and a son (of G). S2 is a son.
  4. Fathers: G and S1, which is 2. Sons: S1 and S2, which is 2. Grandfather: G, which is 1.
  5. All conditions hold with 3 persons. A grandfather needs a child and a grandchild in the group, so at least 3 persons are needed. Hence 3 is the minimum.

Answer: (C) 3

Exam tips

  • Write B and G on rough paper and form equations. This is faster than reading the story again and again.
  • Check the options first. If only one fits all statements, you can stop after testing it.
  • Watch for 'cannot be determined'. Use it when a gender word like cousin or spouse is the only clue.
  • In 'minimum persons' questions, try to merge compatible roles before counting.
  • With 0.25 negative marking, skip a very long puzzle on the first pass and return if time remains.

Practice questions from Blood Relations

Counting Persons and Gender Determination: frequently asked questions

How do I find gender in blood relation problems?

Look at the relation word. Father, son, brother, uncle and husband are male. Mother, daughter, sister, aunt and wife are female. Words like cousin, parent and spouse do not fix gender, so wait for another clue.

How do I count sons and daughters in these questions?

Let B be boys and G be girls. A boy has B − 1 brothers and G sisters. A girl has B brothers and G − 1 sisters. Form equations from the statements and solve.

Can one person have two relations in the same puzzle?

Yes, if the roles are compatible. One man can be a father and a son at the same time. This matters in minimum-member questions, where you merge compatible roles to get the smallest group.

Are there negative marks for blood relations questions?

Yes. Paper 3 Quantitative Aptitude carries 0.25 marks of negative marking per wrong answer. Attempt a question only when you can eliminate options or reach a clear answer.