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
$$\eqalign{ & \Rightarrow \frac{{\left( {100 - r} \right)}}{{100}} \times \frac{{\left( {100 + r} \right)}}{{100}} \times x \cr & \Rightarrow x = \frac{{100 \times 100}}{{\left( {100 - r} \right)\left( {100 + r} \right)}} \cr & \Rightarrow x = \frac{{10000}}{{\left( {10000 - {r^2}} \right)}} \cr} $$
Related Questions on Percentage
A. $$\frac{1}{4}$$
B. $$\frac{1}{3}$$
C. $$\frac{1}{2}$$
D. $$\frac{2}{3}$$
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