Question 844163
p = original price.


Decrease 20%.
{{{p-p(20/100)=p(1-1/5)}}}
{{{(8/10)p}}}


Decrease 25% from (8/10)p.
{{{(8/10)p-(25/100)(8/10)p}}}
{{{(8/10)p(1-25/100)}}}
{{{(8/10)p(3/4)}}}
{{{(8/10)(3/4)p}}}
{{{(4/5)(3/4)p}}}
{{{highlight_green((3/5)p)}}}


The 20% and then the 25% decreases were effectively a decrease of {{{(2/5)}}} of the original price, which is a 40% decrease from the original price p.  


The question is, starting from {{{(3/5)p}}}, what is the percent increase to reach {{{1*p}}}?


Let m be a factor so that {{{(3/4)p*m=p}}}.  What is the value of this factor, m?  No steps needed hopefully, for seeing that {{{highlight_green(m=5/3)}}}.  As the percent increase, this is {{{m=5/3=1&2/3}}}; the two-thirds part being the fraction of the increase needed.  As a percentage, this is {{{highlight(66&2/3)}}} percent increase.