The price of a product is P. A shopkeeper raises its price by X% and then offers a discount of Y% on the raised price. The discounted price again becomes P. If Y is the difference between X and Y, then find X.

Let the cost price of the article be Rs.100.
The shopkeeper raises the price by x% and then decreases it by y%.
As a result, he reaches the cost price of the article. 
Also, it has been given that y is the difference between y% and x%.
$$y = x-y$$
$$2y = x$$
We know that $$(1+2y)(1-y)*100 = 100$$
$$(1+2y)(1-y) = 1$$
$$1-y+2y-2y^2 = 1$$
$$2y^2-y=0$$
$$2y = 1$$
$$y = 1/2$$ or $$0.5$$
$$x = 2y$$ 
=> $$x = 1$$ or $$x = 100$$%
Therefore, option D is the right answer.