In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years…
2025
In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, the present age of A is:
- A.
48 years
- B.
50 years
- C.
60 years
- D.
55 years
Show answer & explanation
Correct answer: A
Concept: In two-person age problems spanning past, present, and future, define one unknown for each person's present age (or link both ages through the given age difference), translate every "X years ago" and "in Y years" phrase into (present age plus or minus years) at that same reference point, then solve the resulting system of linear equations.
Let B's present age = x years. Since A is 9 years older than B, A's present age = x + 9 years.
"In 10 years, A will be twice as old as B was 10 years ago" becomes: (x + 9 + 10) = 2(x - 10).
Simplify the equation: x + 19 = 2x - 20.
Solve for x: 2x - x = 19 + 20, so x = 39. This is B's present age.
A's present age = x + 9 = 39 + 9 = 48 years.
Cross-check: 10 years ago B was 39 - 10 = 29 years old, and twice that is 58. In 10 years, A will be 48 + 10 = 58 years old - the two match, confirming the present age of A is 48 years.