Number of points of discontinuity of  $f\left(x\right)=\left\{\frac{x}{5}\right\}+\left[\frac{x}{2}\right]inx\in [0,100]$ is/are (where [.] denotes greatest integer function and {.} denotes fractional part function) 

$\frac{x}{5}$  is integer at 21 points in [0, 100] 
$\frac{x}{2}$  is integer at 51 points in [0, 100]
$\therefore$  but when ‘x’ is a multiple of 10 then f(x) is continuous, 
So that respective points should be subtract from both i.e., multiple of 10 are 11 points in [0, 100]
21 + 51 – 11 – 11 = 72 – 22 = 50