Data Sufficiency

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Pls tell me the simple method to solve this problem.
I applied the logic as below: (this logic was applied after the test when I has suffeceint time to think):
1. To answer the question I basically need to know whether (r/b+w+r)>(w/b+w+r)?
2. Since b is common no need to think about it, hence the 1st statement indirectly says that (r/w)>(w/r).
3. If this is the case it means that r>w and hence it is clear that (r/b+w+r)>(w/b+w+r) is true. SUFFECIENT

Statement 2 is NOT SUFFECIENT. No need to explain it.

But I wanted to know, is there any simpler method to this than applying the above logic?

You are right in saying that the question is:
Is (r/b+w+r)>(w/b+w+r) ?
or
Is r > w?

To understand Statement(1) better, let's add 1 on both LHS and RHS,
r/(b + w) + 1 > w/(b + r) + 1
(r + b + w)/(b + w) > (r + b + w)/(b + r)
Since the numerators are same, Denominator of LHS < Denominator of RHS
b + w < b + r
w < r
SUFFICIENT

Here is a slightly different approach, in case you are not able to see Aneesh's elegant approach of adding 1 to both sides of the inequality.

Dabral