Fathers age and daughter's age add up to 55. Daughters

The fastest solution would be to test the answer choices. Here's why:
The father's age is the reverse of the daughter's age, and the answer choices represent the daughter's age.
So, if the daughter is 16 years old (answer choice C), then the father is 61, which means the sum of their ages will be clearly greater than 55. Eliminate C.
If the daughter is 17 years old (answer choice D), then the father is 71, which means the sum of their ages will be clearly greater than 55. Eliminate D.
If the daughter is 18 years old (answer choice E), then the father is 81, which means the sum of their ages will be clearly greater than 55. Eliminate E.
If the daughter is 15 years old (answer choice B), then the father is 51, which means the sum of their ages = 15 + 51 =66. No good; the question tells us the sum of their ages is 55. Eliminate B.

By the process of elimination, the correct answer must be A.