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

Let the Father be x years when he died.
Average Age 10 years ago be A.
Total Age 10 years ago = 6 × A
Total Age after 10 years(Just before father's Death) = 6A + 6 × 10 = 6A + 60
Father Died and Baby was born => the Total number of people in the family is Same (6)
Baby born today so age of baby = 0
(6A + 60 - x)/6 = 6A/6
=> A + 10 -(x/6) = A
=> x/6 = 10
=> x = 60
Therefore we can conclude that the father was 60 years old when he died.