Let $y$ be the speed of work of a robot per hour and $S$ be the total amount of work done.
$\frac{5}{7}$ of work is completed in $39$ days with $7$ hours a day. So,
$\frac{5}{7}S = 125 \times 39 \times y \times 7 \to(1)$
Remaining work = $\frac{2}{7}S$ and now we have $13$ more days and $8$ hours per day. So,
$\frac{2}{7}S = x \times 13\times y \times 8 \to (2)$
where $x$ is the number of robots required.
$(1) /(2) \implies \frac{5}{2} x \times 8=125\times 3\times7 .$
$x = \frac{1050}{8} = 131.25.$
So number of robots required $=\lceil 131.25 \rceil = 132$. We have $125$ already and so the no. of additional robots required $= 132-125 = 7.$