A person’s present age is one-third of the age of his mother. After 12 years,…
2025
A person’s present age is one-third of the age of his mother. After 12 years, his age will be one half of the age of his mother. What is the present age of his mother?
- A.
30
- B.
34
- C.
38
- D.
36
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Correct answer: D
Concept: In a relative-age problem, assign a variable to one person's present age using the given ratio, then write an equation for the future condition (each person's age increases by the same number of years) and solve the resulting linear equation.
Application:
Let the son's present age be x years; since his age is one-third of his mother's, the mother's present age is 3x years.
After 12 years, the son's age is (x + 12) and the mother's age is (3x + 12).
The son's age after 12 years is one-half of his mother's age at that time, so (x + 12) = 0.5(3x + 12), which rearranges to (3x + 12) = 2(x + 12).
Expanding: 3x + 12 = 2x + 24, so x = 12.
The mother's present age is 3x = 36 years.
Cross-check: Present ages are 12 and 36 (ratio 1:3, as required). After 12 years they become 24 and 48 — 24 is exactly half of 48, confirming the condition holds.
Answer: The mother's present age is 36 years.