The average age of a man and his daughter is 45 years. If the ratio of their ages after 9 years is 23 to 13, find the present age of the daughter.

The daughter's present age is 30 years.

Sum of ages now = 2 x 45 = 90 years.

After 9 years each grows, so the sum = 90 + 18 = 108.

Ratio 23:13 has 36 parts, so one part = 108/36 = 3.

Daughter after 9 years = 13 x 3 = 39; present = 39 - 9 = 30.