Father is four times the age of his daughter. If after 5 years, he would be…

Concept: In a multi-stage age problem, represent the unknown present ages with a single variable, translate each future condition given in the question into a linear equation by adding the same number of years to every person's present age, solve for the variable, and only then compute the ratio at the checkpoint the question actually asks for.

1. Let the daughter's present age be x years. Since the father is four times her age, the father's present age is 4x years.

2. After 5 years, the daughter's age is (x + 5) and the father's age is (4x + 5). The question states that at this point the father's age is three times the daughter's age, so 4x + 5 = 3(x + 5).

3. Expanding and simplifying: 4x + 5 = 3x + 15, which gives x = 10.

4. So the daughter's present age is 10 years and the father's present age is 40 years.

5. "Further after 5 years" means 5 more years after the first checkpoint, i.e. a total of 10 years from now. At that point the daughter's age is 10 + 10 = 20 years and the father's age is 40 + 10 = 50 years.

6. Required ratio = father's age / daughter's age = 50 / 20 = 2.5 times.

Cross-check: at the first checkpoint (5 years from now), father's age = 40 + 5 = 45 and daughter's age = 10 + 5 = 15. Their ratio is 45 / 15 = 3, which matches the condition given in the question, confirming x = 10 is correct.

Hence, 10 years from now, the father's age is 2.5 times the daughter's age.