text: Examveda
  
  # 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 :
  
  A. 5000
  
  B. 5050
  
  C. 5500
  
  D. 5900
  
  Let the original number be $$x$$
  = 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}
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