If the exchange rate for dollar-to-pound and pound-to-dollar is the same (dependent upon 'x' in this case) then the 1000 dollars would ideally remain the same (if there is no commission) after being converted to pounds and back to dollars.
But, there is a commission levied in this case (which is dependent upon 'y' here). So, in both the exchange operations, the guy has to shell out some money which is ONLY DEPENDENT UPON 'y'.
Therefore, statement (A) which talks about 'x' is useless, and statement (B) which talks about 'y' is SUFFICIENT.
The answer is, thus, B.
P.S. We don't need to calculate the calculate the money left. We just need to make sure that we have enough data to calculate that.
Alternatively:
Let's say that your money gets multiplied by 'k' when you convert from dollar to pound and divided by 'k' when it is converted back into dollars. (Note that k = x/100, as per the question)
Then, your 1000 dollars become 1000k pounds. If the commission of 'y%' is levied then 1000 dollars become 1000k.(1 - y/100) pounds first and then 1000(k/k).(1 - y/100).(1 - y/100) dollars later, or 1000.(1 - y/100)^2 dollars.
This shows that the final amount is independent of k (or the exchange rate) but is only dependent on 'y'.
So, the answer is B.
