Father and twin sons: The average age of a father and his two twin sons is 30 years. If the ratio of the father’s age to one son’s age is 5 : 2, find the father’s current age.

Introduction / Context:We have one parent and two children with an average and a ratio. Transform the ratio into algebraic expressions and use the average to get the exact ages.

Given Data / Assumptions:

• Average of three = 30 → total = 90
• Father : one son = 5 : 2
• Sons are twins, so both have the same age

Concept / Approach:Let one son be S and father be (5/2)S. With two sons, total = (5/2)S + 2S = (9/2)S = 90. Solve for S, then compute the father’s age.

Step-by-Step Solution:

Verification / Alternative check:Totals: father 50, sons 20 and 20 → sum 90, average 30, ratio 50 : 20 = 5 : 2, all conditions met.

Why Other Options Are Wrong:

• 30, 45, 20, 40: inconsistent with both the ratio and the total 90.

Common Pitfalls:Treating the 5 : 2 ratio as 5 : 4 for two sons; the ratio is stated for one son, then doubled separately when summing ages.

Final Answer:50 yr