Total Time needed to execute the program = $120ns$
1. Since Stage Delays are different, Each stage will effectively take as much time as the slowest stage i.e. $10ns$
2. After $FI$ stage of $I_5$, in the very next cycle, $I_8$ instruction will enter into the pipeline (Doesn't mean $I_5$ will go to next stage in next cycle Since it is mentioned in the question that it will not be executed, So, I guess some "Flush" mechanism must be there to flush it out of the pipeline.)
So, Now this Question is pretty straightforward and we need to make instructions $I 1,2,3,4,5,8,9,10$ enter into the pipeline without any stall/delay between consecutive instructions. Thus, Total execution time = (5 + 7) * 10 ns = 120ns.
Note : When Stage Delays are Different, Each stage will effectively take as much time as the slowest stage.
Refer Previous GATE Questions, There are many on this concept.
https://gateoverflow.in/330/gate2013-45?show=330#q330