Sum in the future, ratio in the present: A father is currently twice his son's age. After 5 years the sum of their ages will be 85. What are their present ages?

Introduction / Context:We combine a present-day multiplicative relation with a future sum condition. One variable (the son) is enough, since the father's age is expressed in terms of it.

Given Data / Assumptions:

• Let son's present age be s; father's present age is 2s.
• After 5 years: (s + 5) + (2s + 5) = 85.

Concept / Approach:Translate the future sum to a linear equation in s and solve directly.

Step-by-Step Solution:1) 3s + 10 = 85.2) 3s = 75 ⇒ s = 25.3) Father's present age = 2s = 50.

Verification / Alternative check:After 5 years: 30 + 55 = 85, which matches the condition.

Why Other Options Are Wrong:Other pairs do not produce a future sum of 85 under the present “twice” relation.

Common Pitfalls:Forgetting that both ages increase by 5 when forming the future sum.

Final Answer:50, 25