The problem in the image can be broken down as follows:

• 10 years ago, the person got married and their wife became the 6th member of the family.
• Today, the person's father died and a baby was born, so the family still has 6 members.
• The average age of the family today is the same as it was 10 years ago.
• We are asked to find the age of the father when he died.

Let's define some variables:

• Let $S_0$ be the total sum of the ages of the family members at the time of the marriage (10 years ago).
• Let $S_1$ be the total sum of the ages today.
• Let the age of the father 10 years ago be $f$.
• Let the father's age today (when he died) be $f+10$.

Step-by-step Analysis:

1. Sum of ages 10 years ago:

   • There were 6 family members at the time of marriage.
   • Total sum of their ages was $S_0$.
   • The average age then was $\frac{S_0}{6}$.

2. Sum of ages today:

   • The father passed away, but a baby was born.
   • The sum of ages today is the sum of the ages of the remaining family members plus the new baby (age 0).
   • The sum today is still $S_0 + 60$, because each of the original 6 members (including the father) has aged by 10 years.
   • The average age today is $\frac{S_1}{6} = \frac{S_0 + 60}{6}$.

3. Equality of average ages:

   • The problem states that the average age today is the same as it was 10 years ago.
   • Thus, $\frac{S_0}{6} = \frac{S_0 + 60 - (f+10)}{6}$.
   • Simplifying this gives: $S_0 = S_0 + 50 - f$.
   • Therefore, $f = 50$.

So, the father was 60 years old when the marriage took place, and he died 10 years later, at 70 years old.

The correct answer is 70.

Would you like further clarification or details on this problem?

Here are some additional related questions:

1. How does the average age of a group change over time with the addition of new members?
2. How can this type of problem be solved using algebraic methods?
3. What is the significance of the average remaining the same after a time period?
4. How would the answer change if the father had died a year earlier?
5. What if the baby born was not a newborn, but 2 years old?

Tip: Whenever dealing with averages, remember that the total sum divided by the number of members gives the average. Keep this basic relation in mind for various situations!