Question 891683
Let L = the older brother's present age
Y = the younger brother's present age

"two years ago I was three times older than my brother" <==> L - 2 = 3(Y - 2), and
"In three years I will be twice older than my brother" <==> L + 3 = 2(Y + 3).

the first equation is equivalent to L - 3Y = -4, while the 
second equation is equivalent to L - 2Y = 3.

Solving this system gives Y = 7.
Thus, the younger brother is 7 years old.