The incident took place on April 13 when the girl appeared for her college exam at Dharampeth Polytechnic College, which was her examination center. The victim studies in a different polytechnic college, police said.
According to police, the accused Amit Ganvir had caught the girl copying during the exam.
"The girl later complained that the accused, Amit Ganvir, who is the lecturer at Dharampeth Polytechnic College and was the supervisor in her exam hall, had snatched her identity card, exam hall ticket and her mobile phone during the exam," in-charge of Ambhazari police station, inspector Atul Sabnis told PTI.
She also said that later on he demanded sexual favours from her, following which she approached the police and lodged a formal complaint against him.
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Sabnis said that the accused has been booked under IPC section 354 (assault or criminal force to woman with intent to outrage her modesty).
Earlier in the day, Shiv Sena workers blackened the face of the accused and took him to the police.
"After we received a complaint from the girl's friends about the lecturer, we approached the Principal of the college this afternoon and demanded action against him. However, since no action was taken, we blackened his face and took the accused to Ambazari police station," Shiv Sena activist Panju Totwani said.