Though aditya has given a good algebric explanation,here is another take.I hope it will also help u understand!
when u say a:b:c=3:4:7,it doesn't mean values of a,b,c are 3,4,7...It can be 3,4,7 or 6,8,14 or 9,12,21 and so on..It just means the simplest ratio between terms are in 3:4:7.
So stmt (1) alone is not sufficient.
c-a=12 doesnt tell us their values.So stmt(2) alone is not suffiient.
Combing these two, if we assume a,b,c are 9,12,21.these values satisfy both stmts, hence assumption is correct.
We get a,b,c as 9,12,21 by multiplying the ratio by 3.