M19-13

Question

Initially, 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 charged on each exchange operation, what is the remaining dollar amount after both exchanges?

(1) $x = 0.6$

(2) $y = 5$

Show Answer

Official Answer

B

(1)  x = 0.6 
 
(2)  y = 5

Bunuel · Accepted Answer

Official Solution:

Initially, 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 charged on each exchange operation, what is the remaining dollar amount after both exchanges? 
 
Note that,  x  pounds = 1 dollar, means that 1 pound =  \frac{1}{x}  dollars (for example, if 0.5 pounds = 1 dollar, then 1 pound = 1/0.5 = 2 dollars.)
 
First, when 1000 dollars are converted into pounds at  x  pounds per dollar, with a commission of  y\% , we get  1000*x*(1 - \frac{y}{100})  pounds. Then, when  1000*x*(1 - \frac{y}{100})  pounds are converted back into dollars at  \frac{1}{x}  dollars per pound, with a commission of  y\% , we get  1000*x*(1 - \frac{y}{100})*\frac{1}{x}*(1 - \frac{y}{100})=1000(1 - \frac{y}{100})^2 . As we can see, since we convert twice at the same exchange rate, the exchange rate does not matter, and only the commission is important. So, to answer the question, we can ignore  x  and are interested only in the value of  y .
 
(1)  x = 0.6 
 
The statement above tells us the value of  x , not  y . Not sufficient.
 
(2)  y = 5 
 
The statement above tells us the value of  y . Sufficient.

Answer: B

Senthil7 · Answer

I think this is a  high-quality  question and I agree with explanation.

chetanyasahu1 · Answer

I think this is a  high-quality  question and the explanation isn't clear enough, please elaborate. I agree with the impact of Y on exchange but what about x, once the exchange operation is done what about the loss through exchange rate, I believe that should also be converted.

reynaldreni · Answer

CASE #1 Exchange Rate X = 0.6 (£0.6 = $1)
• $1000 --> £600
• (-) Commission 5%  £570
• £570--> $950
• (-) Commisson 5%  $902.5

CASE #2 Exchange Rate X = 2 (£2 = $1)
• $1000 --> $2000
• (-) Commission 5% --> £1900
• £1900 --> $950
• (-) Commisson 5% --> $902.5

SO, exchange rate does not matter.

JIAA · Answer

Xylan

Sorry to bother you again!
Instead of calculating exchange difference at the first exchange and then at the second exchange, can we approach the Q in the following manner instead???

exchange rate => £x = $1

first exchange with y% commission = $1000 = £1000x(y/100) = £10xy

second exchange with y% commission = (10xy/x)(y/100) = $ y^2/10

Q is asking what dollar amount was left after the exchanges?

Hence, we need to know value of y. Does this make sense ??

XyLan · Answer

JIAA  It's a   beautiful   Question,  attacking  the conscience of the test taker who is in a  hurry .

Few things to keep in mind:  
  Correctly  inferred from the Q-statement:   exchange rate => 
   $   1 =   £    x   
   £   1 =   $    1/x    
 If a commission of  y % is levied on any exchange operation, then the remaining amount( amount that is left after the commission-cost ) should be  Amount*(1 - y/100)

1st exchange with  y% commission  with starting amount:  
  $  ------->  £  
   $    1000  ------ leads to ------>   £    1000*(1 - y/100)*x

2nd exchange with  y% commission  with starting amount:    
  £  ------->  $  
   £    1000*(1 - y/100)*x  ------ leads to ------>   $    1000*(1 - y/100)^2 :   the value of  x  cancels out

Since the  value of X  cancels out, only  Y's value  is  required  to answer the Q.

ImranBinkhaled · Answer

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.

RenanBragion · Answer

I think this is a  high-quality  question and I agree with explanation.

coreyander · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

smegha668 · Answer

I like the solution - it’s helpful.

M19-13

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