A neighbour found Savitri lying in a pool of blood when she went to her house to give 'prasad', police said.
Savitri lived with her 10-year-old granddaughter Suman in her house while her two sons Subhash and Sunder reside with their families in Mayur Vihar and Vaishali, respectively.
Her husband passed away in 2012, they said.
The minor girl was in school and Savitri was alone in the house at the time of incident.
According to the complaint, some jewellery and cash are missing from the house.
Prima facie it appears that she may have been murdered for resisting a robbery bid, he said.
A case has been registered and the matter is being probed further.