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 :

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