A father is 30 years older than his son. He will be three times as old as his…

Concept: In age-relationship problems, assign a variable to one person's present age, express the other person's present age in terms of it using the given age gap, then translate 'after n years' by adding n to each age. The stated ratio at that future time gives one linear equation in the variable, which is solved directly.

Application:

1. Let the son's present age be s years. Since the father is 30 years older, the father's present age is s + 30 years.

2. After 5 years, the father's age is (s + 30) + 5 = s + 35, and the son's age is s + 5.

3. The given condition states the father's age after 5 years is three times the son's age at that time: s + 35 = 3(s + 5).

4. Expanding: s + 35 = 3s + 15.

5. Rearranging: 35 - 15 = 3s - s, so 20 = 2s, giving s = 10.

6. The father's present age is therefore s + 30 = 10 + 30 = 40 years.

Cross-check: With father's present age 40 and son's present age 10, the gap is 40 - 10 = 30 years, matching the given condition. Five years later the father is 45 and the son is 15, and 45 = 3 × 15, confirming the ratio condition holds.