The father of girl is three years older than his mother, Six years ago, the average of the girl and her parents was 32 years, and the age of the father was twice the present age of his daughter, What is the present age (in years) of the mother?

Let the present age of the girl is 'x'   So, the age of the father six years ago was '2x' The age of the girl six years ago was 'x - 6' The father of a girl is three years older than his mother. So, the mother's age was '2x - 3' The total age of the girl and her parents six years ago was 32 × 3 = 96 years The total age of the girl and her parents six years ago was 2x + 2x - 3 + x - 6 = 96 years 5x = 96 + 9  5x = 105  x = 21 The age of mother six years ago was 2x - 3 = 2 × 21 - 3 = 39 years The present age of mother will be 39 + 6 = 45 years