From the circuit shown below, the maximum and minimum value of zener diode current are :

The Zener diode acts as the voltage regulator in the circuit and the voltage supply is variable hence, excess of voltage over $50V$ will be across $5K\Omega$ resistance.

Thus, minimum voltage across $5K\Omega$ resistance is $80V-50V=30V$ 

Current through $5K\Omega$ resistance is $I_1$(say)

$I_1=\frac{30}{5000}=6mA$

Also, maximum voltage across $5K\Omega$ resistance is $120V-50V=70V$ 

Current through $5K\Omega$ resistance is $I_1^{\prime }$...(say)

$I_1^{\prime }=\frac{70}{5000}=14mA$

Now, voltage across load resistance of $10K\Omega$ is $50V$

Thus, current through $10K\Omega$ will be
$I_2=\frac{50}{10000}=5mA$

Hence, maximum current through Zener diode is
$I_z=I_1^{\prime }-I_2=14-5=9mA$   

Minimum current through Zener diode is
$I_z=I_1-I_2=6-5=1mA$