When I was married 10 years ago, my wife became the sixth member of the family.\nToday my father has died and a baby has been born to me.\nThe average age of the family at the time of my marriage is the same as the average age today.\nWhat was my father's age when he died?

Introduction / Context:
This is a well known average age puzzle that mixes changes in family composition with the concept of constant average. When the average age of a group stays the same over a period in which everyone grows older, there must be compensating changes such as deaths and births. We use this idea to find the father s age at death.

Given Data / Assumptions:

• At the time of marriage (10 years ago), the wife became the sixth member of the family, so there were 6 members at that time.
• Ten years have passed since the marriage.
• Today, the father has died and a baby has been born, so the number of family members is still 6.
• The average age of the family at the time of marriage is equal to the average age of the family today.
• We must find the father s age at the time of his death (which is today in the story).

Concept / Approach:
Let the total age of the 6 family members at the time of marriage be S years. The average then is S / 6. After 10 years, if all 6 original members were still alive, each would be 10 years older, so the total age would be S + 6 * 10 = S + 60. However, the father dies and a newborn baby of age 0 joins. We then use the fact that the average today is still S / 6, which means the total age today is still S. From this, we can solve for the father s age 10 years ago and then find his age at death.

Step-by-Step Solution:
Let S be the total age of the 6 family members at the time of marriage. Average age at marriage = S / 6. Ten years later, if no one left or joined, each of the 6 would be 10 years older. Total age then would be S + 6 * 10 = S + 60. At this time, the father dies. Suppose the father s age at marriage was F years. So his age today would have been F + 10 if he had not died. After his death, we remove F + 10 from the total. A newborn baby of age 0 joins, so nothing is added to the total for age. Thus total age today = (S + 60) - (F + 10) = S + 50 - F. Given that the average age today equals the average at marriage, the total today must equal S. So we set S + 50 - F = S. This simplifies to 50 - F = 0, hence F = 50. Thus the father was 50 years old at the time of the marriage (10 years ago). His age at death today is F + 10 = 60 years.

Verification / Alternative check:
At marriage, the father was 50 and there were 5 other family members with some ages adding to S - 50. Ten years later, if all were alive, their total age would be S + 60. Removing the father age of 60 leaves S. Adding a newborn with age 0 keeps the total S, so the average remains S / 6, exactly as at the time of marriage. This confirms the internal consistency of the solution.

Why Other Options Are Wrong:
If the father had died at 50, 65 or 70, the total today would not match the original total S, so the average would change. Only 60 satisfies the condition that the total and hence the average age remains unchanged despite ten years passing and changes in family membership.

Common Pitfalls:
A common mistake is to assume that the family size changed, when in fact it remains at 6 members throughout. Others mis-handle the ten year increment or forget to remove the father s age and add the baby s age correctly. Working explicitly with total sums and keeping a clear timeline usually prevents these errors.

Final Answer:
The father was 60 years old when he died.