Answer
25 Joules
Work Step by Step
As we know that
$W_{total}=W_{gravity}+W_{w}$
Where $W_{total}$ is the total work done while $W_{gravity}$ and $W_{w}$ represent Work done by gravity and Work done by worker respectively.
First of all we calculate work done by the worker $(\theta=180^{\circ} )$ because the direction of motion of block and force applied by worker are opposite
$W_{w}$=$F d$$cos 180^{\circ}$
$W_{w}$=$50\times{0.5}(-1)$
$W_{w}$=$-25J$
$W_{total}=W_{gravity}+(-25)J$
As we know that total change in $K.E$ is in fact total work done so
$80J$=$W_{gravity}-25J$
$W_{gravity}$=$80+25J$
$W_{gravity}$=105J
If the rope had not been attached then the work done would be just due to gravity that is $105J$ and it would be $25J$ greater than current $K.E$ which is 80J.i.e $105-80=25J$
