A father is five times as old as his son, but after 15 years, he will be only…
2023
A father is five times as old as his son, but after 15 years, he will be only twice as old as his son. What is the age of the father?
Answer: B. 25 years — ConceptIn age problems, the age difference between two people remains constant, while each person’s age increases by the same number of years. When one…
- A.
20 years
- B.
25 years
- C.
30 years
- D.
More than one of the above
- E.
None of the above
Attempted by 10 students.
Show answer & explanation
Correct answer: B
Concept
In age problems, the age difference between two people remains constant, while each person’s age increases by the same number of years.
When one present age is a multiple of another, represent both ages with one variable and translate the future-age relation into a linear equation.
Application
Let the son’s present age be x years. Then the father’s present age is 5x years.
After 15 years, their ages will be x + 15 and 5x + 15 years. The future relation gives 5x + 15 = 2(x + 15).
Expanding and simplifying: 5x + 15 = 2x + 30, so 3x = 15 and x = 5.
Therefore, the father’s present age is 5x = 5 × 5 = 25 years.
Cross-check
At present, the ages are 25 and 5 years, and 25 ÷ 5 = 5.
After 15 years, the ages become 40 and 20 years, and 40 ÷ 20 = 2. Both conditions hold, so the father is 25 years old.