The ages of two brothers are in the ratio two to three, but in eight years, the ratio of their ages will be three to four. what is the age of the older brother?

 let x = age of younger bro 
ley y = age of older bro 

x/y = 2/3 > x = 2y/3 eq.1 
x+8 / y+8 = 3/4 eq.2 

sub eq.1 into eq.2: 

(2y/3) + 8 / y+8 = 3/4 
(2y+24)/3 / y+8 = 3/4 
2y + 24 / 3(y+8) = 3/4 
2y+24 / 3y+24 = 3/4 
4(2y+24) = 3(3y+24) 
8y+96 = 9y+72 
24=y 

x=2y/3=2*24/3=16

Source- https://answers.yahoo.com/question/index?qid=20090519120852AA85lSu