The question displayed in the image is as follows:

"When I was married 10 years ago my wife was the 6th member of the family. Today my father died and a baby is born to me. The average age of my family during my marriage is the same as today. What is the age of my father when he died?"

Solution Approach:

Let’s break this down step by step:

1. Initial Information:

   • When the man was married 10 years ago, the family had 6 members.
   • Now, the father has passed away, and a baby has been born, keeping the family size the same at 6 members.
   • The average age of the family is the same today as it was 10 years ago.

2. Let the Variables Represent:

   • $A_0$: Total age of the family members 10 years ago.
   • $n = 6$: Number of family members 10 years ago and today.
   • The average age 10 years ago is $\frac{A_0}{n}$.

3. Change in Age After 10 Years: Over 10 years, each family member has aged by 10 years. So, the total increase in age for all family members would be $6 \times 10 = 60$ years.

4. New Total Age of Family Today: Since the father died and a baby was born, we need to account for this:

   • The total age of the family today (with the father dead and baby born) is the same as 10 years ago.
   • Let the father’s age at the time of death be $F$.
   • The baby’s age is 0.

   So, the total age of the family today is: $(A_0 + 60) - F + 0 = A_0$ This simplifies to: $60 - F = 0$ $F = 60$

Conclusion:

The father’s age when he died was 60 years.

Would you like any further explanation or details on this? Let me know if you'd like to explore other aspects of this problem.

Here are 5 related questions that expand on this topic:

1. How does the average age of a family change with births and deaths over time?
2. If the family size had changed more dramatically, how would that affect the calculation of average age?
3. How can we account for situations where multiple members join or leave a family?
4. What would happen if the father had died before the baby was born—how would the total change in age be calculated then?
5. How would you solve this if the father’s death and baby’s birth were not on the same day?

Tip: When dealing with average age problems, always consider the impact of changes in the number of family members and whether the changes in total age compensate for each other.