The price of a hat is reduced by a% from its regular price, and then is raised by a% from the reduced price. If the resulting price is an 81% discount from the regular price, what is a?
I will let a be the decimal (not the %) discount.
New price = P'
Original price = P
P' = (1-a)P*(1+a) = 0.19 P
(81% final discount)
Then
1 - a^2 = 0.19
a = 0.9
The "a" discount is 90%