Find the value of $$\frac{1}{5} + $$   $$999\frac{{494}}{{495}} \times 99$$   = ?

Solution (By Examveda Team)

$$\eqalign{ & \Leftrightarrow \frac{1}{5} + 999\frac{{494}}{{495}} \times 99\, \cr & \Rightarrow \frac{1}{5} + \left[ {999 + \frac{{494}}{{495}}} \right] \times 99\, \cr & \Rightarrow \frac{1}{5} + \left[ {999 + 1 - \frac{1}{{495}}} \right] \times 99 \cr & \Rightarrow \frac{1}{5} + \left[ {1000 - \frac{1}{{495}}} \right] \times 99 \cr & \Rightarrow \frac{1}{5} + 99000 - \frac{1}{5} \cr & \Rightarrow 99000\, \cr} $$