The age difference between my son and me is 30 years. In 3 years from today, I will be thrice as old as my son. What is my age now?
A) 12
B) 42
C) 38
D) 45
E) 15

Question

The age difference between my son and me is 30 years. In 3 years from today, I will be thrice as old as my son. What is my age now? 
A) 12
B) 42
C) 38
D) 45
E) 15

Quizplus · Accepted Answer

Let's denote the current age of the son as $S$ and the current age of the parent as $P$. According to the problem, $P = S + 30$. In 3 years, the parent will be $P + 3$ years old, and the son will be $S + 3$ years old. At that time, the parent will be thrice as old as the son, so $P + 3 = 3(S + 3)$. Substituting the first equation into the second gives $S + 30 + 3 = 3S + 9$, simplifying to $33 = 2S + 9$, and then $24 = 2S$, so $S = 12$. Therefore, the parent's current age is $S + 30 = 42$.

The Age Difference Between My Son and Me Is 30