A mother is 46years old and her son is 21 years old in the year 1997. In what year was the mother six times as old as the son?

Age of the mother in the year 1997 = 46years
Age of her son in the year 1997 = 21years
x years ago, age of the mother = 46 - x.
x years ago, age of the son = 21 - x.
Hence by the given condition,
46 - x = 6(21 - x)
46 - x = 126 - 6x
-x + 6x = 126 - 46
5x = 80
x = 16
Thus the year was 1997-16 = 1981.