Total work to be completed in $52$ days &, there are $125$ identical robots , each works for $7 \hspace{0.1cm } hrs/day$
Assuming, Total work is $W$
As each robot is working for $7 \hspace{0.1cm } hrs/day$
each day $125$ robots completed a total of $125 \times 7\hspace{0.1cm }W$
In 39 days $\dfrac{5}{7}\hspace{0.1cm }W$ is completed
∴ $125 \times 7 \times 39 = \dfrac{5}{7}\hspace{0.1cm }W$
Or, $W = \dfrac{125 \times 7 \times 7 \times 39 }{5}$
∴ Total Work = $47775$
∴ $\dfrac{5}{7}W = \dfrac{5}{7} \times 47775$
$\qquad= 34125\hspace{0.1cm } W $ is completed already in $39$ days
Remaining Days = $(52-39)$ = $13$
∴ In $13$ days $(47775 - 34125)$ = $13650\hspace{0.1cm } W$ has to be done
In $13$ days $125$ Robots can complete
$13 \times 125 \times 8 = 13000\hspace{0.1cm } W$ $\qquad[\text{Now each robot works for 8 hrs/day]}$
∴ Remaining = $(13650-13000)$ = $650\hspace{0.1cm } W$
The remaining $650\hspace{0.1cm } W$ can be completed by $\dfrac{650}{13 \times 8} = 6.25 \approx 7$ robots in $13$ days