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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?

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. \(y = 5\)

Dollar to pounds $1000 = 1000x pounds after commission = 1000x (100 - 5%) pounds = 950x pounds

Pounds to Dollar 950x pounds = 950x (1/x) dollar = 950 dollar after commission = 950 dollar (100 - 5%)= 95% of 950 dollar

I was thinking without any calculations that since the exchange rate did not change x is irrelevant. However Y is still essential.

If you are running out of time on the math session, just pick B and move on.

If you have some time to spare, then you verify with calculation.

topmbaseeker 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. \(y = 5\)

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient

You just need to know that if the exchange rate of converting dollar to pound is \(X\), then the exchange of converting pound to dollar is \(\frac{1}{X}\)

B. You don't need to know the exchange rate because it will be equal once you convert it back. you need to know how much they charge between conversions

I have one little problem with the wording of this problem..

It doesn't mention where the y% is applied. Is it applied after conversion or before (on the total amount)? Different assumptions lead to different answers.

First, If you assume the commission is applied to starting amount:

$ --> GBP 1000 --> 1000x-10y

1000x-10y --> 1000-10(y/x) -10xy + (10y^2)/100

Answer is C.

Second, if you assume the commission is applied to final amount $ --> GBP 1000 --> 1000x-10xy

1000 dollars = 1000x GBP after deducting y % commission 1000x-10xy GBP which is nothing but 1000-10y dollars.

again converting back to dollars, divide GBP by x = 1000-10y - commission commission = y% of (1000-10y) dollars =10y - (y^2)/10

so total money left in dollars is 1000 -10y -(10y -(y^2)/10) =1000-20y+(y^2)/10 which is independent of x because this amount is in dollars. So the catch in the very starting is that question asks about dollars. That should be used to save time.

The conversion is from dollar to pound and back to dollar at the same exchange rate (x). In the end, we still have 1000 dollars, so x is not important.

To get the remaining amount after levy: 1000*(1-y%)^2