A family consists of a man, his wife, their four sons, the four sons’ wives, and one daughter. Each of the four sons also has his own family with 3 sons and 1 daughter. Based on this information, how many female members are there in the entire extended family?

Introduction / Context:
This is a counting and family-structure puzzle, often seen in aptitude tests under logical reasoning or arithmetic word problems. You must carefully interpret the description of the generations, identify which members are female, and sum them accurately without double counting or missing any group.

Given Data / Assumptions:

• The first generation: a man and his wife (1 male, 1 female).

• Their children: four sons and one daughter (4 males, 1 female).

• Each son is married, so there are four daughters-in-law (4 females).

• Each of the four sons has 3 sons and 1 daughter in his own family.

• Thus, each son contributes 1 granddaughter (female) to the original couple.

Concept / Approach:
The trick is to categorize all individuals into generations and then count only the female members. We must be systematic: start from the original couple, move to their children, then to the sons’ spouses, and then to the grandchildren. We assume there is no other information such as additional spouses or extra daughters beyond what is mentioned.

Step-by-Step Solution:
Step 1: First generation. The original couple has 1 man and 1 wife. Female count so far = 1 (the wife). Step 2: Children of the original couple. They have four sons (all male) and one daughter (female). Add 1 more female. Total female count now = 1 + 1 = 2. Step 3: Wives of the four sons. Each of the four sons is married, so there are 4 daughters-in-law, all females. Add 4 more females. Total female count now = 2 + 4 = 6. Step 4: Grandchildren from each son. Each son has 3 sons and 1 daughter. Only the daughters are female. There are 4 sons, each having 1 daughter, giving 4 granddaughters in total. Add 4 more females. Total female count now = 6 + 4 = 10. Step 5: Confirm that no other female category exists. The grandsons (3 per son) are all male and do not contribute to the female count.

Verification / Alternative check:
We can summarise quickly: • Original generation: 1 female (wife). • Children generation: 1 daughter + 4 daughters-in-law = 5 females. • Grandchildren: 4 granddaughters. Total females = 1 + 5 + 4 = 10. This matches our detailed step-by-step count, so our reasoning is consistent.

Why Other Options Are Wrong:
Option A (12) overcounts by adding extra females that are not mentioned in the problem statement.
Option B (8) undercounts by forgetting some daughters-in-law or granddaughters.
Option C (9) is one short, likely missing either the original daughter or one granddaughter.

Common Pitfalls:
Candidates often misread the phrase “family of every son also has 3 sons and one daughter” and mistakenly multiply the numbers incorrectly. Others forget to include the original daughter or double-count the sons’ wives. A careful, grouped approach prevents these errors: count females generation by generation and cross-check with a quick summary.

Final Answer:
Therefore, the total number of female members in the family is 10.