Bunuel wrote:
1000 dollars were converted into pounds and then the pounds were converted back into dollars at the same exchange rate of \(x\) pounds per dollar. If a commission of \(y\%\) is levied on any exchange operation, what dollar amount was left after the exchanges?
(1) \(x = 0.6\)
(2) \(y = 5\)
This is an ideal example that emphasizes the importance of understanding every word in the question. If you understand the question, the answer requires a very simple arithmetic calculation of percentages.
From reading the replies to this question, it seems people are making an assumption that currency conversion entails exchange rate loss. Although this is generally true in real life, the question's premise defines the environment otherwise as it clearly states that the DOLLAR and POUND conversions were done at the same rate (both the time). Now read the question again:
"1000 dollars were converted into pounds and then the pounds were converted back into dollars at the same exchange rate of x pounds per dollar. If a commission of y% is levied on any exchange operation, what dollar amount was left after the exchanges?"That is, the only cost to these transactions is the y% commission on exchange operations. This cost was incurred two times- once during conversion from $ to £ and then during conversion from £ to $. So, the end value of the principal amount ($1000) in dollars, after incurring commission 2 times is :
1000(1−y/100)^2
Hope the explanation was easy enough for everyone to understand. More important, please keep the moral of the question in mind.