Answer : Option B

Explanation :

Note: Assume the total work = LCM of the given time

Take the LCM of hours = LCM of (8, 12, and 24) = 24
Let the total work = 24

Note: One hour work = (total work/ time)

Now,

A's one hour work = 24/8 = 3 unit
B's one hour work = 24/12 = 2 unit
C's one hour work = 24/24= 1 unit

ATQ, between 3 am - 4 am, A works alone and finish 3 units of work
Between 4 am - 5 am, A and B work and complete 3+2 = 5 units of work
Between 5 am - 6 am, A, B, and C works and finishes 3+2+1 = 6 units of work

Or, between 3 am to 5 am, 8 unit of work is finished.
Remaining 24-8= 16 unit (till 5am)
After 5 am, A+B+C work together and finish 6 unit of work per hours.

i.e., 6 unit work = 1 hour

To complete the 16 unit work, multiply both sides with 2

i.e., 12 unit work = 2 hours
Remaining work = 16-12 = 4 unit work

As we know, 6 work = 1 hour
Or, 1 work = 1/6 hours
Or, 4 work = 4/6 or 2/3 hours.

That means (2 + 2/3) hours requires after 5 am.

So, time taken to complete the work is (5 +2 + 2/3) = 7:40am