Problems on Ages — “Mother’s age is twice the daughter’s age. Father is 10 years older than mother. Brother is 20 years younger than mother and 5 years older than his sister. Find the father’s age.”

Introduction / Context:Multiple family relations can be solved by expressing all ages in terms of a single variable (typically the youngest). Two independent statements about the brother provide an equation that fixes that variable; the rest follow directly.

Given Data / Assumptions:

• Let daughter = D.
• Mother = 2D.
• Father = Mother + 10 = 2D + 10.
• Brother = Mother − 20 = 2D − 20.
• Brother is 5 years older than sister ⇒ Brother = D + 5.

Concept / Approach:Use the two formulas for the brother to form one equation in D, solve for D, then compute the father’s age.

Step-by-Step Solution:

Verification / Alternative check:Brother = D + 5 = 30, which also equals Mother − 20 = 50 − 20 = 30 ✓. All relations are consistent.

Why Other Options Are Wrong:52/55/58/62 contradict at least one relation once D = 25 is fixed and Mother = 50 is computed.

Common Pitfalls:Mixing “older than” with “younger than”; applying the 10-year adjustment to the wrong parent; overlooking that two independent expressions are given for the brother.

Final Answer:60 years