The ratio of the present ages of a daughter and her mother is 3 : 7. The mother's age at the time of the daughter's birth was 20 years. Find the mother's present age.

Question: The ratio of the present ages of a daughter and her mother is 3 : 7. The mother's age at the time of the daughter's birth was 20 years. Find the mother's present age.

Solution:
Let,
the present ages be 3x and 7x.

At the time of daughter's birth (0 years old), the mother's age = mother's age - daughter's age.
∴ Difference in ages = 7x - 3x = 4x.

Given that,
The difference in ages is 20 years.
∴ 4x = 20
⇒ x = 5.

Mother's present age = 7x = 35 years.