Mother’s age is twice her daughter’s age. The son is older than daughter by…
20172017
Mother’s age is twice her daughter’s age. The son is older than daughter by one year and father is five years older than mother. If son has completed 18 years, find father’s age.
- A.
39 years
- B.
40 years
- C.
41 years
- D.
42 years
Attempted by 28 students.
Show answer & explanation
Correct answer: A
Age-relationship word problems are solved by assigning ONE variable to a single person's age, then translating every stated relationship (“twice as old”, “X years older/younger”) into an algebraic expression in that same variable. The one numeric age given in the problem closes the system, letting you solve for the variable and then compute every other age in the chain.
Let the daughter's age be D years.
The son is older than the daughter by one year, so the son's age = D + 1.
The son has completed 18 years, so D + 1 = 18, which gives D = 17.
The mother's age is twice the daughter's age: Mother = 2 × 17 = 34 years.
The father is five years older than the mother: Father = 34 + 5 = 39 years.
Cross-check: with father = 39, mother = 39 − 5 = 34 (matches “five years older”); daughter = half of 34 = 17 (matches “twice as old”); son = 17 + 1 = 18 (matches “older by one year” and the given age). Every relationship in the statement is satisfied.
Father's age = 39 years.