Tabulated form of the data:

S - Source station D - Destination Station

Extra time taken if flight is the mode of travel = 3 hours(Road trip) + 1 hour(early arrival)
Option (A):
Source is Jamshedpur(AI9810)
Time of departure from home = 8:00 - 4 hour = 4:00
Arrival time at Delhi = 9:45
She can depart by flight earliest by 9:45 +1:30(Airport to work) + 6:00(Work time) + 1:30(Work to Airport) + 1:00(Early Arrival) = 19:45
IT3347 departs from Delhi at 17:10. So, she reaches Jamshedpur by 18:55(2nd day) + 3:00(Road Trip) = 21-55(2nd day)
Total Time = 41 hours 55 mins.
Option (B):
Starting from Jamshedpur (AI9810) = 4:00
Arrival time at Delhi = 9:45
She can depart by train earliest by 9:45 +1:30(Airport to work) + 6:00(Work time) + 00:30(Work to station) + 0:05(Wait time) = 17:50
Train 12802 departs from Delhi(RS) at 22:10 and reaches Jamshedpur by 20:05(2nd day).
Total time = 40 hours 5mins.
Option (C):
Starting from Jamshedpur = 19:20 - 4 hour = 15:20
Arrival time at Delhi = 21:05
She can depart by flight earliest by 21:05 +1:30(Airport to work) + 6:00(Work time) + 1:30(Work to Airport) + 1:00(Early Arrival) = 7:05(2nd day)
AI9809 departs from Delhi at 5:50. So, she can reach Jamshedpur by 7-35(3rd Day) + 3:00(Road Trip)=10:35(3rd Day)
Total Time = 43 hours 15mins.
Option (D):
Starting from Jamshedpur = 15:55
Arrival time at Delhi (RS) = 10:35(2nd day)
She can depart from Delhi (RS) earliest by 10:35(2nd day) + 00:30(Station to Work) + 0:05(Wait time) + 6:00(Work time) + 00:30(Work to station) + 0:05(Wait time) = 17:45(2nd day)
Train 12444 departs from Delhi (RS) at 17:20. So she will catch the train the next day.
Since the total hours is more than 48, this is not the answer,
Option (E):
Starting from Jamshedpur = 4:00
Arrival at Delhi airport = 9:45
She can depart from Delhi (RS) earliest by 9:45 + 1:30(Airport to work) + 6:00(Work time) + 00:30(Work to station) + 0:05(Wait time)= 17:50
So, she can start only on day 2 at 17:20.
Thus, since she will be out for more than 48 hours, this is not the correct answer.
Thus, the correct answer is B.