One year ago, the father was four times as old as his son. Six years from now, the father will be 9 years more than twice his son’s age. What is the ratio of their present ages (father : son)?

Introduction / Context:
We have two time-shifted linear relations: one from the past comparing father to son by a factor, and another from the future comparing father to twice the son plus a fixed number. Solve these equations to obtain current ages and then simplify the ratio.

Given Data / Assumptions:

• One year ago: F − 1 = 4(S − 1).
• Six years later: F + 6 = 2(S + 6) + 9.
• Find present ratio F : S.

Concept / Approach:
Form linear equations in F and S and solve. The presence of constants (−1, +6, +9) requires careful algebra to avoid mistakes.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

Common Pitfalls:

Final Answer:
11 : 3