The woman, also a rag-picker, was found dead in Ghatkopar here on January 1, they said.
Police had first registered a case of accidental death, but later converted it into an FIR by applying charges of rape, unnatural sex murder after the findings in the post mortem report.
Last night Pant Nagar police arrested Aarif Sheikh (21), Raju Jaiswal (21) and Milind Tayde (22), all local rag pickers who were acquainted with the victim.
On the night of December 31, the accused consumed liquor at Rasika Bar, a few minutes away from the spot on Ghatkopar-Andheri Link Road, where her body was found.
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The three then went to the woman where Arif allegedly forced himself upon her, followed by the others.
Fearing that the accused might complain to the police, the men hit her on the head with a stone and fled the scene.
After the police initiated investigations, they rounded up all local rag-pickers in the area for questioning when they learnt of the trio and Arif's relations with the victim.
Police are now awaiting medical and DNA reports to ascertain the involvement of the accused in the crime.