Age of mother = 31 years
Age of daughter = 7 years
Lets suppose that after X years,
mother's age will be three by two times that of daughter's age.
After X years,
Age of Mother = (31 + X) years
Age of Daughter = (7 + X) years
According to the question,
(31 + X) = 3/2 (7 + X)
=> 62 + 2X = 21 + 3X
=> 3X - 2X = 62 - 21
=> X = 41
Lets verify the value of X = 41,
Mother's age after 41 years = 31+41 = 72
Daughter's age after 41 years = 7+41 = 48
Ratio of ages of mother and daughter is 72 : 48 = 3 : 2 which satisfies the statement that after 41 years, mother's age will be three by two times of the daughter's age.
