Where exactly I am going wrong here? 
A can of juice was $80\%$ full. $80\%$ of the contents were emptied
  into a glass and $81$ ml of juice was added to the can. Then the can
  became full to the brim. What is the capacity of the can ?

If $x$ ml be the full capacity of the can then $$\frac 4{25}x + 81 = x$$ but then solving for $x$ from here won't give $225$ ml which is the required answer for this problem.  What exactly I am missing here?
 A: Unless I made a mistake in my own algebra/logic- what you have seems to make sense to me. So, I would say that the answer is wrong. Here is my way of doing things:


*

*Capacity= $x$

*Original amount of juice: $0.8 \ x$

*Amount discarded: 80%

*Thus, juice left in can: $0.8 \ x \ 0.2$

*Amount added to fill up to brim: 81 ml 

*Thus, we have:
$$ 0.8 \ x  \times \ 0.2 + 81 = x$$
which is the same as yours.
A: To obtain the given solution requires $\rm\ F (1-E) = 0.64 = (225-81)/225,\ $ where $\rm F$ is the initial fraction of full, and $\rm E$ is the fraction emptied, e.g. $\rm F = 0.8,\ E = 0.2\:.\:$ So it appears that the problem should say all but $80\%$ were emptied.
A: As was noted in the comments below, something is wrong with the question.  $x$ would be 225 if the equation was $\frac{64}{100}x+81=x$.  It seems that what was meant was the contents in the glass (which is 80% of 80% of the can) plus 81 mL (from somewhere else) fills the can.  (Sorry for my initially incorrect response.)
A: if $x$ is the capacity of a can.
stage 1: $80$% of x is in the can: $0.8x$
stage 2: $80$% of the content is emptied: $0.8x-(0.8x)0.8$
stage 3: $81$ ml is added back to the can $0.8x-(0.8x)0.8+81$
final: can is full $x$
overall 
$
0.8x-(0.8x)0.8+81 = x
$ 
Solving this equation, $x$ is around $94$ml can not be $225$ml as the answer in the book.
I think there must some other interpretation of the original question.
