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 Ballia - RAJDHANI EXP (20503).

Muzaffarpur to Ballia RAJDHANI EXP (20503) departs from Muzaffarpur Jn station (MFP) at 19:40 and arrives Ballia station (BUI) at 22:55. This train has 3 stoppages. Muzaffarpur to Ballia rajdhani fare is Rs.1405 in First AC, Rs.875 in Second AC and Rs.645 in Third AC for this train which includes meal charges also.