# The ages of a mother and a daughter are 31 and 7 years respectively. In how many years will the mother’s age be 3/2 times that of the daughter?

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The ages of a mother and a daughter are 31 and 7 years respectively. In how many years will the mother’s age be 3/2 times that of the daughter?

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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.

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