A number is first decreased by 10% and then increased by 10%. The number so obtained is 50 less than the original number. The original number is :

Answer: Option A

Let the original number be $$x$$
Final number obtained :
= 110% of (90% of $$x$$)
= $$\left(\frac{110}{100}\times \frac{90}{100}\times x\right)$$
= $$\frac{99x}{100}$$
$$\begin{array}{rl}& \therefore x-\frac{99x}{100}=50\\ & \Rightarrow \frac{x}{100}=50\\ & \Rightarrow x=50\times 100\\ & \Rightarrow x=5000\end{array}$$