There's an even faster way...
Step 1. Essentially write out the problem.
.7A + .5B= 6.3
Step 2. Multipy both sides by 10
7A + 5B = 63
Step 3. Look at both coefficients, 7 and 5. 7 goes nicely into 63, so you isolate the equation in terms of A.
7A = 63 - 5B
A= 9 - 5B/7
Step 4. Looking at this equation you know B, which is bananas has to be a multiple of 7. So B could equal 7, 14, 21, etc. But when you look at the answer choices, none of them are greater than 14 and if B = 14 that means A would have to equal 0 (again based on answers given, which would be impossible.) So therefore B has to equal 7 which means A equals 4 and so A + B equals 11.
Answer B