Father–son ratio over time – A father is five times as old as his 6-year-old son. After how many years will the father be four times as old as his son?

Introduction / Context:
Here we are given a current multiplier and asked to find when a different multiplier will hold in the future. Setting up the linear-in-time equation for both ages and solving for the time variable gives the answer swiftly.

Given Data / Assumptions:

• Son's present age S = 6.
• Father's present age F = 5 × 6 = 30.
• Find t such that F + t = 4(S + t).

Concept / Approach:
Use the standard “after t years” linear relation. Both people age at the same rate (+t), so only the intercepts differ.

Step-by-Step Solution:
30 + t = 4(6 + t) = 24 + 4t.30 − 24 = 4t − t ⇒ 6 = 3t ⇒ t = 2.Therefore, in 2 years, father will be four times the son’s age.

Verification / Alternative check:
After 2 years: father 32, son 8, and 32 = 4 × 8.

Why Other Options Are Wrong:
Other values of t do not satisfy the future 4× relation.

Common Pitfalls:
Forgetting that both ages increase by the same t or incorrectly scaling the future ages.

Final Answer:
2 years