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 :

A. Rs. 1

B. Rs. $$\left( {\frac{{1 - {r^2}}}{{100}}} \right)$$

C. Rs. $$\frac{{\sqrt {1 - {r^2}} }}{{100}}$$

D. Rs. $$\frac{{10000}}{{\left( {10000 - {r^2}} \right)}}$$

Answer: Option D

Solution(By Examveda Team)

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