A software company sets up $$m$$ number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took 8 more days to finish the assignment. The value of $$m$$ is equal to:

We need to find the value of $$m$$ (number of computer systems) so that the assignment is completed in 25 days after crashes.

Total work = $$17m$$ system-days since $$m$$ systems would complete it in 17 days.

With 4 systems crashing at the start of each subsequent day:
Day 1: $$m$$ systems working
Day 2: $$m - 4$$ systems
Day 3: $$m - 8$$ systems
$$\vdots$$
Day $$k$$: $$m - 4(k-1)$$ systems

The total work done in 25 days is $$\sum_{k=1}^{25}[m - 4(k-1)] = 25m - 4\sum_{k=0}^{24}k = 25m - 4 \cdot \frac{24 \times 25}{2} = 25m - 1200$$.

Setting this equal to the total work gives $$25m - 1200 = 17m$$, so $$8m = 1200$$ and thus $$m = 150$$.

The correct answer is Option (1): 150.