They said the woman, Sudhir Bansal, was accompanying her son, Gaurav, who recently enrolled in Delhi University, to help him find accommodation.
They boarded the Yoga Express from Rajasthan. Sudhir was standing near the door of a compartment. When the train slowed down near the Mithai Pul, on the way to the railway station, a person caught hold of her bag, the police said.
The woman tried to fight him off but lost her balance and fell down on the tracks. She came under the wheels of the train and was injured, the police said.
The person fled with the bag containing cash, some documents and an ATM card.
The woman's body was handed over her relatives after an autopsy who took it to their hometown in Bhiwadi in Rajasthan, the police said.