The price of an articles was increased by r%. Later the new price was decreased by r%. If the latest price was Rs. 1, then the original price was :

Answer: Option D

Let the original price be Rs. $$x$$
∴ (100 - r)% of (100 + r)% of $$x$$ = 1
$$\begin{array}{rl}& \Rightarrow \frac{\left(100-r\right)}{100}\times \frac{\left(100+r\right)}{100}\times x\\ & \Rightarrow x=\frac{100\times 100}{\left(100-r\right)\left(100+r\right)}\\ & \Rightarrow x=\frac{10000}{\left(10000-r^2\right)}\end{array}$$