%ages

[AJWILL]

Bill is having $2000 in his bank account as on 30th May, 2008.At the start of every month he deposits A% of the amount that was present in his account.At the end of every month he withdraws B% of the month that was present in his account.He follows the same process 4 times.At the end of this process, the total amount in his account is $2000.Then which of the following is true ?, given that no other transaction takes place in his account.
[A] A < B
Depends only value of A
[C] A = B
[D] A > B
[E] Depends on the value of B

[tisrar02]

This is how I would do this problem and correct me if i'm wrong:

If Bill has $2000 in his bank account and deposits A% each month and withdraws B% each month and gets the same amount as when he started, I believe the answer should be A>B

Similar example:

$100 in your bank account
Deposit A%=25%
Bank balance= $125

Now to get back to $100, we need to withdraw B%=20%--> 125*80%=$100

Therefore A>B IMO:D

What's the OA?

[eagleeye]

Bill is having $2000 in his bank account as on 30th May, 2008.At the start of every month he deposits A% of the amount that was present in his account.At the end of every month he withdraws B% of the month that was present in his account.He follows the same process 4 times.At the end of this process, the total amount in his account is $2000.Then which of the following is true ?, given that no other transaction takes place in his account.
[A] A < B
Depends only value of A
[C] A = B
[D] A > B
[E] Depends on the value of B

We know that Bill starts off with 2000 and ends up with the same amount.
The first process is in two steps:
Bill adds A% , so new money = 2000*(1+A%)
Bill removes B%, now the money = 2000*(1+A%)(1-B%)
So after 4 of these iterations, he has 2000*(1+A%)^4*(1+B%)^4.
Since this equals 2000, We need ((1+A%)(1-B%))^4 = 1
=> (1+A%)(1-B%) = 1 (we discard the negative sign because, he can't take out more than he has)
=> (1+A/100)(1-B/100) = 1
=> (100+A)/100 * (100-B)/100 = 1
=> (100+A)(100-B) = 100*100
=> 100^2 + 100A -100B -AB = 100^2
=> 100(A-B) = AB
=> A-B = AB/100
=> A = B+AB/100.

clearly A is greater than B (by AB/100).

Hence D is correct.

[[email protected]]

Hi AJWILL,

In questions like these, it makes sense to take an easy
number into consideration since %age is applicable in the same way to
100 as to 2000.
2000 is just a distraction.
Also we do not need to calculate for 4 times,

If A = 20%
Then increased amount = 120

Now once he withdraws the amount has to come back to the original,
because say if he gets to 105 after withdrawal considering A and B remain constant
then the last figure will always be > 100. (Please correct me if I am wrong)

Hence
Bill withdraws (20/120)% = 16.67%
Hence A>B .. Ans is D