My brother is three times as old as me. How many times my age now was his age when I was born?
It is a question invented as a puzzle for kids (!) by Igor Vladimirovich Arnold (1900-1948). I am not a kid anymore and am having a lot of difficulty in solving it. I am confused now. I guess it's because I was never exposed to this kind of question (I dunno). It's for kids, so it should be simple, but the wording does a knot in my brain somehow.
Let $b$ denote the age of your brother, and $m$ denote your age. Your brother is 3 times as old as you, so $$b = 3m.$$
When you were born, your brother's age was $$b' = b-m.$$
So, $$\frac{b'}{m} = \frac{b-m}{m} = 3-1 = \bf{2}.$$
Your brother's age when you were born is twice your age now.