You have two large 2 liter container and a small cup of unknown volume. At the beginning you have 1.2 liter of acid solution of unknown concentration in the left container, and 0.9 liter pure acid in the right one. We take one cup of solution from the left container and putting it into the right one. After that we take one cup of the resulting solution from the right container and put into the left container. Finally we again put one cup solution from the left container into the right one. At the end, we have 50% acid solution in the left container and 80% acid solution in the right one. How large is the cup, and what was the initial acid concentration in the left container?
Erich Prisner, August 2003