A father is three times as old as his son. In 15 years he will be twice as old as his son. What are their present ages?
Son 15, father 45. Let the son be x and the father 3x. In 15 years: 3x + 15 = 2(x + 15), so x = 15.
Explain it simply
Both people age by the same number of years, so the gap between their ages never changes. That one fact solves most age problems. Here the gap is 2x now (3x - x), and in 15 years the father is twice the son, which means the gap then equals the son's age then.
Example
Question: Father = 3 x son now. In 15 years, father = 2 x son. Present ages?
- Son = x, father = 3x.
- In 15 years: 3x + 15 = 2(x + 15) = 2x + 30.
- x = 15. Son 15, father 45.
Gap view: the gap is 30 years and never changes. "Twice as old" means the gap equals the son's age at that time, so the son will be 30, which is 15 years from now at age 15.
Check: 45 + 15 = 60 and 15 + 15 = 30. 60 = 2 x 30.
const x = 15;
console.log([x, 3 * x, (3 * x + 15) / (x + 15)]); // Output: [15,45,2]What to say in the interview
"I let the son be x and the father 3x, then add 15 to both and set the father to twice the son. That gives x equals 15, so 15 and 45. The constant age gap is a quick cross-check."
Common mistakes
- Adding 15 to only one person.
- Doubling the son's present age instead of his future age.