Sum after 5 years and fixed difference – Jais and his father differ by 35 years now. After 5 years, their ages will sum to 125. What will their ages be 12 years from now?

Introduction / Context:
This problem provides a present-time difference and a future-time sum and asks for another future-time pair. Solve present ages first, then advance to the requested time.

Given Data / Assumptions:

• Let J = Jais now, F = father now.
• F − J = 35.
• (J + 5) + (F + 5) = 125 ⇒ J + F = 115.

Concept / Approach:
From J + F = 115 and F − J = 35, add to get 2F = 150 ⇒ F = 75 and J = 40. Then add 12 years to both for the asked time.

Step-by-Step Solution:
F = 75, J = 40.After 12 years: J = 52, F = 87.

Verification / Alternative check:
After 5 years: J = 45, F = 80 → sum 125, as given. Difference now 75 − 40 = 35, as given.

Why Other Options Are Wrong:
They do not arise from the unique present pair (40, 75) advanced by 12 years.

Common Pitfalls:
Using the 35-year difference at the future time incorrectly (differences stay constant across equal increments, but sums do not unless specified).

Final Answer:
52 and 87