Percentage Problem #1

Question

Can any one explain with solution plz

In any month Mr.Sam deposits m% and withdraws n% of the closing balance of the previous month. If his balance at the end of March ( after the withdrawal) is the same as his balance at the begining of January ( before deposit), which of the following is true?

A) n/2 n
D) m < n/2
E) m= n + 25

jamifahad · Answer

Let the closing balance of December be x.
Also, this closing balance will be opening balance for January (before deposit)

January 
Deposit = m% of closing balance of December
= xm/100
Balance = x+xm/100

Withdrawal = n% of closing balance of December
=xn/100

Hence Closing Balance at the end of January = x + xm/100 - xn/100
= x 
Let 1+0.01m-0.01n =A
Closing Balance at the end of January = xA

February 
Deposit = m% of closing balance of January
= xAm/100
Balance = xA + xAm/100

Withdrawal = n% of closing balance of January
= xAn/100

Hence Closing Balance at the end of February = xA + xAm/100 - xAn/100
=xA 
= xA^2 ( since 1+0.01m-0.01n =A)

March 
Deposit = m% of closing balance of February 
= xA^2 m/100
Balance = xA^2 + xA^2m/100

Withdrawal = n% of closing balance of February
= xA^2n/100

Hence Closing Balance at the end of March = xA^2 + xA^2m/100 - xA^2n/100
=xA^2 
= xA^3 ( since 1+0.01m-0.01n =A)

Closing balance of March = Opening balance of January
=> xA^3 = x
=> A^3=1
=> 1+0.01m-0.01n=1
=> 0.01m=0.01n
=> m=n

OA B

ctkrishnan · Answer

One doubt over here.. how is A^3 =1 and in the next step the cube is gone??? It has been directly equated to 1..??
Should not it be (1+0.01m-0.01n)^3 = 1???

jamifahad · Answer

Question states that Closing balance of March = Opening balance of January

Closing balance of March = xA^3
Opening balance of January = x

Equating, x * A^3 = x
Canceling x from both sides. A^3 =1

Yes. Take cube root both sides.
Cube root of 1 will be 1.
hence 1+0.01m-0.01n = 1

Hope i made it clear.

ctrlaltdel · Answer

This definitely must be 700+ level question.....is there any easier\shortcut way to solve this.

ctkrishnan · Answer

Yes.. got it.. thanks!

Sudhanshuacharya · Answer

Guys not sure, but my approach was a bit different. I actually did not calculate the solution.
Here goes:

The question says that the person deposits m% and withdraws n% on the same amount.
Hence net balance will always be X + (m-n)X/100

So if m> n, then his net bank balance should increase, whereas if n>m his bank balance should decrease.

As at the end of 3 months period the principal amount remains same therefore m=n

Hence B.

cleetus · Answer

Thanks for making it more clear. Thanks for making me aware once again that most of the questions in GMAT can be solved through Common Sense. :-)

cleetus · Answer

Thanks for explaining the concept. U deserve a kudo :-)

manishgeorge · Answer

The question states that his balance does not change over the period of three months

So Amount he with draws is equal to the amount he deposits. So M = N

bumpbot · Answer

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Percentage Problem #1

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