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**.