I am having headaches whenever question requires choosing base appropriately when manipulating percentage related problems. I am sure I have not made any sense so far, so let me choose an example problem first:
A number is increased by $20\%$ and then again increased by $20\%$. By what percent should the increased number be decreased so as to get back the original number?
My initial solution was like:
Let there be number $x$ which is increased sequentially twice by $20\%$. So the difference between increased number and init number $x$ would be: $120\% 120\% x - x $.
Now what to choose as base (increased number or init number $x$ ?) to make the ratio (part to whole) and then convert it in to percent?
This was just an example of problem I often face, so I would welcome any concepts/analogy which will make whole base selection procedure easy. Thanks.
Always consider a "percent increase" of $n$ as multiplying the current number by $1 + n/100$, and a "percent decrease of $n$ as multiplying the current number by $1 - n/100$.
Always use the last calculated number as a "base". In this case, suppose your number is 100. Increasing it by 20% twice gives you 144. Then, calculate the percentage that 144 needs to be decreased to bring it back to 100, which is about 30.55%, rather than the 44% you might have gotten by using 100 as the "base".