The value of an investment increases by x% during January and decreases by y% during February. If the value of the investment is the same at the end of February as at the beginning of January, what is y in terms of x ?

A) 200x/100 + 2x

B) x(2 + x)/(1 + x)2

C) 2x/1 + 2x

D) x(200 + x)/10,000

E) 100-(10,000/100 + x)

Answer is E).

I found this on a CAT exam, and I understand the explanation in the solution. However, I tried solving the equation in different ways and I do not get the same answer. Please help.

These are my calculations:

I(1+x/100)(1-y/100)=I

(1+x/100)(1-y/100)=1

1-y/100+x/100-xy/10,000=1 (I distributed the 2 equations)

x/100-xy/10,000-y/100=0

x/100=xy/10,000+y/100

x=xy/100+y (I multiplied denominators by 100)

100x=xy+100y ( I multiplied denominator by 100 again to cancel it out)

100x=y(x+100)

100x/(x+100)=y

The denominator is correct, but not the numerator. Where did I go wrong?