Question

Can someone explain this problem to me?? After a price reduction of x%, an item has its price increased to its original value. What was the percent of increase? Express your answer as a common fraction in terms of x.

Answer 1

`We\ are\ given\ that,\\Percent\ of\ reduction=x_-\\So,\\Let\ the\ percent\ of\ increase\ be\ x_+\\Let\ the\ original\ price\ of\ the\ item\ be\ y\\Let\ the\ price\ after\ the\ decrease\ be\ z\\.\\Hence,\\y-(x_-)/(100) =z\\ z+(x_+)/(100)=y\\By\ simply\ adding\ the\ equations,\\(y+z)+(- (x_-)/(100)+(x_+)/(100))=(z+y)\\Hence,\\- (x_-)/(100)+(x_+)/(100)=0\\Hence,\\ (x_-)/(100)=+(x_+)/(100)\\Hence,\\x_-=x_+\\`

`Hence,\ the\ percent\ of\ increase\ is\ same\ as\ the\ percent\ of\ decrease.`