Q:

How to calculate how a percentage scales up?

Sorry i know this is probably a very stupid question.
But given a pie,
Let us say we have 3 slices of 50%, 30% and 20%
now at each iteration i remove one slice (starting from the big one)
so after removing the first slice of 50%, i am now left with two slices, but they are no longer 30% and 20% as they now need to make up 100% again, so they "turn" into 60% and 40% respectively.
after the next slide is removed (60%) there is only one slice left which is now 100% (the entire pie)
given any combination of percentages, how can i calculate (given the example above) that the previously 30% slice should now be 60% after the 50% slice is removed?
can you give a calculation example for
50%, 30% & 20%
as well as:
35% 35% 30%
Thanks!

A:

The total you have after removing the first $50\%$ is $100-50=50\%$.
So, what was $30\%$ earlier is now $30\%$ of $50\%$, i.e., $\frac{30}{50}\times 100 = 60\%$. Similarly, the $20\%$ of the full pie from before is now $20\%$ of $50\%$, which gives $\frac{20}{50}\times 100 = 40\%$.
As another example, for the $35-35-30$ case, once you remove $35\%$ of the pie, you have $35\%$ of $100-35=65\%$, and $30\%$ of $65\%$.

