Family ages with fixed differences: A father is 30 years older than his first son, and the first son is 10 years older than the second son. If the sum of their present ages is 95 years, find the father’s current age.

Introduction / Context:Linear age chains with fixed differences are straightforward: define the youngest as a variable, express others relative to it, and use the given total to solve. This avoids ratio complications.

Given Data / Assumptions:

• Let the second son be y.
• First son = y + 10.
• Father = y + 40 (since 30 more than first son).
• Total of three ages = 95.

Concept / Approach:Sum the three expressions and solve the resulting one-variable linear equation.

Step-by-Step Solution:1) y + (y + 10) + (y + 40) = 95.2) 3y + 50 = 95 ⇒ 3y = 45 ⇒ y = 15.3) Father = y + 40 = 15 + 40 = 55 years.

Verification / Alternative check:First son = 25; second son = 15; father = 55. Sum = 55 + 25 + 15 = 95 (correct). Differences match the problem.

Why Other Options Are Wrong:

• 45/50/65/60 years make the total or differences inconsistent with the statement.

Common Pitfalls:Mixing up the direction of differences (who is older) or mis-summing the three expressions can lead to errors.

Final Answer:55 years