Answer: The son was 30 years old when he was a quarter of his father's age.
Step-by-step explanation:
Assuming the father's current age is F and the son's current age is S.
Given that the father was 30 years old when his son was born, there is a 30-year age difference between them: F - S = 30.
After a certain period of time, the son's age becomes a quarter of the father's age.
Let's represent the time that has passed since the son was born as T. At that point, the son's age is S + T and the father's age is F + T.
Using the information provided, we can express the son's age (S + T) as a quarter of the father's age (F + T): S + T = 1/4 * (F + T).
By substituting F - S = 30 (from step 2) into the equation, we get: S + T = 1/4 * (S + T + 30).
Simplifying the equation further: 4(S + T) = S + T + 30, which leads to 3S = 3T + 30.
From the equation, we find that the son's age (S) equals the time that has passed (T) plus 10.
To determine the age at which the son was a quarter of his father's age, we need to find a value of T that satisfies the equation S = T + 10.
By setting T = 20, we find that S = 20 + 10 = 30. This means the son is 30 years old when he is a quarter of his father's age.
Therefore, we can conclude that the son was 30 years old when he reached a quarter of his father's age.