# How to choose appropriate “base” when manipulating problems pertaining to percentages?

I am having headaches whenever question requires choosing base appropriately when manipulating percentage related problems. I am sure I haven't made any sense so far, so lemme choose a 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 init 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'd welcome any concepts/analogy which will make whole base selection procedure easy . Thanks

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It would be better to just consider the increased value of $x$, namely $1.2\cdot1.2\cdot x$ (not the difference). If this increased value is decreased by $y\%$, the final value is $(1-y/100)\cdot(1.2\cdot1.2\cdot x)$. But you know this later value is just $x$. So you have $(1-y/100)\cdot(1.2\cdot1.2\cdot x)=x$. Now solve this for $y$ (note the $x$'s cancel). – David Mitra Jan 31 '13 at 14:06

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 $1 - n/100$.
will you theory apply to this question : If A's salary is 20% less than B's salary. By how much percent is B's salary more than A's ? ? – Mr.Anubis Jan 31 '13 at 14:16