Where exactly I am going wrong here?

Question

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?

Answer 1

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.

Answer 2

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.)

Answer 3

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:

1. Capacity= $x$

2. Original amount of juice: $0.8 \ x$

3. Amount discarded: 80%

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

5. Amount added to fill up to brim: 81 ml

6. Thus, we have:

$$ 0.8 \ x \times \ 0.2 + 81 = x$$

which is the same as yours.

Answer 4

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.