A museum offers four video programs that run continuously

First notice the minimum amount of time that needs to be taken: 15+10 + 30+10 + 45+10 + 40 = 160 mins
So D and E are out.
Since all show timings are a multiple of 5 and the group needs 10 mins to regroup, there is no way we will get 164. Hence the only options that will work out are 165 or 160.
If 160 is the answer, we have no wriggle room. We must watch shows one after the other with only 10 mins in between.

Shows: 15 mins, 30 mins, 40 mins, 45 mins
If we start with 15 min show and then regroup in 10 mins, we need to start another show in 25 mins. But no show starts in 25 mins so let's not start with 15 mins. (Same logic can be used to show that we cannot watch 40 min and 45 min shows first if we want to spend a total of only 160 mins)

If we start with 30 min show and then regroup in 10 mins, we need to start another show in 40 mins. A show does start in 40 mins so let's watch that. Now 80 mins have passed. We take 10 mins to regroup and now 90 mins have passed. Both the other shows start now. We watch the 45 min show and regroup for 10 mins. Now 145 mins have passed. But the 15 min show will start in 5 mins so we will need to wait another 5 mins for it and then watch it.
Total time taken will be 165 mins.

We cannot watch all the shows in 160 mins.

Answer A