Averages & Ratios — “The average of father and son is 22. Their age ratio is 10 : 1. What is the son’s age?”

Introduction / Context:
Average gives the sum; ratio splits that sum proportionally. This allows quick calculation without solving simultaneous equations explicitly.

Given Data / Assumptions:

• Average(F,S) = 22 ⇒ F + S = 44.
• F : S = 10 : 1.

Concept / Approach:
Let F = 10k and S = k. Then 10k + k = 11k = 44 ⇒ k = 4. Hence S = 4.

Step-by-Step Solution:

Verification / Alternative check:
Father = 40, Son = 4 ⇒ average = (40 + 4)/2 = 22; ratio 40:4 reduces to 10:1.

Why Other Options Are Wrong:
6/14/24/40 do not satisfy both the sum 44 and the 10:1 ratio simultaneously.

Common Pitfalls:
Dividing 44 by 10 or 1 directly; forgetting that the ratio represents proportional parts of the sum.

Final Answer:
4