I got married 10 years ago, and my wife became the 6th member of our family at…

Concept

Average = Total age ÷ Number of members. When a family's membership changes — one member leaves and is replaced by a newcomer — but the average age stays the same across a fixed time gap, the natural aging of every original member over that gap must be exactly cancelled out by removing the leaving member's age and adding the newcomer's age.

Step-by-step solution

1. Let A be the average age of the family 10 years ago, when it had 6 members (the wife had just become the 6th member).

2. Total age of the family 10 years ago = 6 × A.

3. If none of the original 6 members had left, each would be 10 years older today, so the total age today would have been 6A + 6 × 10 = 6A + 60.

4. Today, the father is no longer part of the family and a baby has joined, so the family still has 6 members; let x be the father's age when he died.

5. The baby's age today is 0, so today's actual total age = 6A + 60 − x.

6. The problem states today's average is still A, so today's total age must equal 6 × A.

7. Equate the two expressions for today's total age: 6A + 60 − x = 6A.

8. Solve for x: 60 − x = 0, so x = 60.

Cross-check

Substitute x back: today's total = 6A + 60 − 60 = 6A, so today's average = 6A ÷ 6 = A — exactly the average given for 10 years ago. The equation balances, confirming the value.

Answer

The father was 60 years old when he died.