Four years ago, the age of the mother was 12 times the age of her daughter. Two years hence, the mother's age will be 4 times the daughter's age. After how many years will the mother's age be 3 times that of her daughter?

Let the present age of the daughter be x years. Four years ago, the age of the daughter = (x - 4) years Four years ago, the age of the mother = 12 × (x - 4) = (12x - 48) years Two years hence, Age of the daughter = (x - 4) + 4 + 2 = (x + 2) years Age of the mother = (12x - 48) + 4 + 2 = (12x - 42) years According to the question, (x + 2) × 4 = (12x - 42)   =4x + 8 = 12x - 42 = 12x – 4x = 42 + 8 8x =50   x = 6.25 Now, the present age of the mother = (12x - 48) + 4 = 12x - 44 = 12 × 6.25 - 44 = 31 Let after y years the age of the mother will be three times that of her daughter. According to the question, (6.25 + y) × 3 = (31 + y) = 18.75 + 3y = 31 + y = 2y = 31 – 18.75   y = 12.25/2   y = 6.125=6(1/8) years. After 6(1/8) years, the mother's age will be 3 times that of her daughter.