A person says: (1) His son is 5 times as old as his daughter. (2) His wife is 5 times as old as his son. (3) He is twice as old as his wife. The sum of their ages (father + wife + son + daughter) equals 81 years, which is the grandmother's age today. How old is the son (in years)?

Introduction:
This question tests forming and simplifying age relations using multiples, then using a total sum to find actual ages. The key observation is that all ages are linked to the daughter via multiplication. Once everything is written in terms of one variable, the total becomes a single equation. Solving that equation gives all ages immediately, and the son's age is one of them.

Given Data / Assumptions:

• Let daughter's age = D years
• Son is 5 times daughter: Son = 5D
• Wife is 5 times son: Wife = 5 * (5D) = 25D
• Father is twice wife: Father = 2 * 25D = 50D
• Total of four ages = 81 years

Concept / Approach:
Express each person's age as a multiple of D, add them, and equate to 81. Then solve for D and compute the son's age = 5D.

Step-by-Step Solution:
Daughter = DSon = 5DWife = 25DFather = 50DTotal = D + 5D + 25D + 50D = 81DGiven total is 81: 81D = 81So D = 1Son = 5D = 5 * 1 = 5

Verification / Alternative check:
With D=1, the ages become: daughter 1, son 5, wife 25, father 50. Their sum is 1 + 5 + 25 + 50 = 81, matching the given total exactly.

Why Other Options Are Wrong:
9, 12, 15, 18: would force daughter to be non-integer or break the fixed multiple chain, and the sum would not stay at 81 under the exact 1:5:25:50 structure.

Common Pitfalls:
Misreading “5 times as old” and writing addition instead of multiplication.Forgetting to include all four people in the total sum.Making “wife is 5 times older” incorrectly as wife = son + 5*son (not needed here).

Final Answer:
5 years