Rajdhani express are premium category trains by the Indian Railways that redefines luxury travelling in India. It is a fully air-conditioned train which connects country capital (Delhi) with state capitals. That is why they are called 'Rajdhani' which translates to 'Capital' in English. These train runs at very high speed and therefore it usually takes least time to reach destination compared to other trains on the same route. Mumbai rajdhani is the fastest rajdhani train which attains a maximum speed of 140 kmph on some stretch. Rajdhani Express offers catering facilities inside the train the fare of which is included in ticket fare. Rajdhani trains have 3 classes - First AC (1A), AC II-tier (2A) and AC III-tier (3A) only and they are coupled with LHB coaches that have higher safety features. The ticket fare for Rajdhani is maximum amongst all trains on the same route and has dynamic fare (Flexi Fare) system. Waitlisted passengers are strictly not allowed inside this train. Rajdhani train coaches are usually painted in red with a grey colored strip outside. 1 rajdhani train runs from Muzaffarpur to Hajipur - RAJDHANI EXP (20503).

Muzaffarpur to Hajipur RAJDHANI EXP (20503) departs from Muzaffarpur Jn station (MFP) at 19:40 and arrives Hajipur Jn station (HJP) at 20:30. This train has 1 stoppages. Muzaffarpur to Hajipur rajdhani fare is Rs.1400 in First AC, Rs.870 in Second AC and Rs.640 in Third AC for this train which includes meal charges also.

The concept of Garib Rath started with the vision to provide air conditioned berths at a comparatively low price for the people who could not afford to travel in AC coaches. Garib-rath phrase translates to poor man's chariot in English. The fare in this train is almost two-thirds of regular third ac fare. Usually Garib Rath have Third AC (3A) class only excepting some 1-2 trains which also have Chair Car (CC) class. The compartments of these train coaches have 9 berths making an extra space for side middle berth which is not there in any other train in India. In case passengers want to have bedrolls they need to pay separately for it. Some garib-raths run as fast as rajdhani, but they have lesser priority for track clearance compared to them. These trains are painted green with a yellow colored strip along the window panes. 2 garib-rath trains run from Muzaffarpur to Hajipur - SHC ANVT GR SPL (05577) and GARIB RATH EXP (12203).

Muzaffarpur to Hajipur SHC ANVT GR SPL (05577) departs from Muzaffarpur Jn station (MFP) at 02:30 and arrives Hajipur Jn station (HJP) at 03:25. This train has 1 stoppages.

Muzaffarpur to Hajipur GARIB RATH EXP (12203) departs from Muzaffarpur Jn station (MFP) at 18:55 and arrives Hajipur Jn station (HJP) at 19:42. This train has 1 stoppages. Muzaffarpur to Hajipur garib-rath fare is Rs.250 in Third AC for this train.

Sampark Kranti is a series of express trains in India that connects different states of India to the national capital - New Delhi. Sampark in Hindi means connectivity while Kranti is also a word in Hindi language meaning revolution. Thus these trains have revolutionized the state connectivity with center. These trains have a combination of all the classes - AC, Sleeper and Unreserved coaches. Sampark Kranti trains are for long distance journeys. These trains are named after states and Sampark Kranti train for a particular state has most of the stoppages in that state only. 1 sampark-kranti train runs from Muzaffarpur to Hajipur - BIHAR S KRANTI (12565).

Muzaffarpur to Hajipur BIHAR S KRANTI (12565) departs from Muzaffarpur Jn station (MFP) at 10:25 and arrives Hajipur Jn station (HJP) at 11:17. This train has 1 stoppages. Muzaffarpur to Hajipur sampark-kranti fare is Rs.1245 in First AC, Rs.750 in Second AC, Rs.545 in Third AC and Rs.175 in Sleeper for this train.