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. 2 rajdhani trains run from Hajipur to Moradabad - RAJDHANI EXP (20503) and RAJDHANI EXP (20505).

Hajipur to Moradabad RAJDHANI EXP (20503) departs from Hajipur Jn station (HJP) at 20:35 and arrives Moradabad station (MB) at 10:47. This train has 6 stoppages. Hajipur to Moradabad rajdhani fare is Rs.3500 in First AC, Rs.2120 in Second AC and Rs.1530 in Third AC for this train which includes meal charges also.

Hajipur to Moradabad RAJDHANI EXP (20505) departs from Hajipur Jn station (HJP) at 20:35 and arrives Moradabad station (MB) at 10:47. This train has 6 stoppages. Hajipur to Moradabad rajdhani fare is Rs.3455 in First AC, Rs.2090 in Second AC and Rs.1515 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 Hajipur to Moradabad - SHC ANVT GR SPL (05577) and GARIB RATH EXP (12203).

Hajipur to Moradabad SHC ANVT GR SPL (05577) departs from Hajipur Jn station (HJP) at 03:30 and arrives Moradabad station (MB) at 21:15. This train has 9 stoppages.

Hajipur to Moradabad GARIB RATH EXP (12203) departs from Hajipur Jn station (HJP) at 19:47 and arrives Moradabad station (MB) at 11:02. This train has 8 stoppages. Hajipur to Moradabad garib-rath fare is Rs.820 in Third AC for this train.