Imagine that we have $s_0$ grams of sugar in a bottle. Then we randomly extract half of the content of the Bottle and replace it with salt.
Let $s_n$ be the grams of sugar inside the bottle after we repeat this $n$ times.
My question is: If we keep doing this, will the number of grams of sugar tend to $0$? This is: is $\lim\limits_{n \to \infty} s_n = 0$?
What if instead of replacing half of the content with salt we replace $k\%$ of it, for any $0 < k < 100$?
What is the expected number of grams after we do this $n$ times?
Your problem misses an important precision : how many grains of sugar/salt ? or some precision about the mixing. If you suppose the number of grains of salt/sugar to be infinite and the mixing to be perfect, then this is no more a probabilistic problem.
$S_n = \frac{s_0}{2^n}$ so its limit is 0.
and with $k$ : $S_n = s_0.k^n$