Present ages from future ratio and given sum — The sum of the present ages of a father and his son is 70 years. Exactly 10 years from now, the son’s age will be one-half of the father’s age then. What are their present ages (Father, Son)?

Introduction / Context:
This is a classic linear-ages setup that mixes a present-time sum with a future-time ratio. We are told the combined present ages equal 70, and in 10 years the son will be exactly half the father. Translating both statements into equations in the present variables is the cleanest approach.

Given Data / Assumptions:

• Let F = father’s present age; S = son’s present age.
• F + S = 70 (present sum).
• After 10 years: S + 10 = (F + 10) / 2.
• All ages are whole years; algebra works regardless of integrality.

Concept / Approach:
Convert the future relation to a present equation and combine with the present sum. From S + 10 = (F + 10)/2, multiply by 2 to avoid fractions and isolate F in terms of S; then substitute into F + S = 70 to solve systematically.

Step-by-Step Solution:
2(S + 10) = F + 10 ⇒ 2S + 20 = F + 10 ⇒ F = 2S + 10.Sum: (2S + 10) + S = 70 ⇒ 3S + 10 = 70 ⇒ 3S = 60 ⇒ S = 20.Therefore F = 2(20) + 10 = 50.

Verification / Alternative check:
In 10 years: son = 30, father = 60; indeed 30 is half of 60. Present sum 50 + 20 = 70, as required.

Why Other Options Are Wrong:
Pairs like 50 & 25 or 47 & 23 do not satisfy both the present sum and the specified future half relation simultaneously.

Common Pitfalls:
Mistaking “son will be half the father in 10 years” for “now,” or misapplying the +10 to only one person. Both ages increase by the same amount when moving forward in time.

Final Answer:
50 years, 20 years