In Kalimpong, Maya D'Souza is a divorced, single mother who runs a cafeteria. Naren Vyas is a reclusive, but brilliant mathematics teacher, who lives next door to Maya and her teenage daughter Tara. Naren is solemn and introverted, though well-liked amongst his students, and his morning exchanges with Maya from whose cafeteria he buys lunch, is the brightest part of his day.

Ajit, Maya's abusive ex-husband and a corrupt policeman, shows up one night to extort money from her which she stole when fleeing from him. He threatens both her and Tara, causing the situation to quickly escalate into violence and Ajit is killed by them via strangulation. Overhearing the commotion from his home and deducing that Ajit has been killed, Naren offers his help to the mother and daughter. He not only disposes the body, but also plots the cover-up step-by-step.

Inspector Karan Anand, a former classmate of Naren, is assigned to track the missing Ajit, which leads him to Kalimpong. There he runs into his old classmate Naren, along with burned remains with Ajit's credentials. Karan's suspicions immediately fall to Maya. Autopsy shows that the murder occurred on the 10th. Maya and Tara have a detailed alibi. Unable to poke any holes in Maya's alibi, Karan is ready to go back. However, one of Maya's employees tells him about Naren's crush on Maya. Karan becomes suspicious of Naren, who had previously claimed to not know Maya very well. Karan finds incriminating evidence against Naren, who does not have an alibi for the 10th.

Maya apologizes to Naren when she finds out what her employee said. She tells him that she clarified to Karan that there is nothing romantic between them. A heartbroken Naren goes to the police station and confesses to Ajit's murder, saying he did it at Maya's behest. Naren starts to frame himself as delusional, setting up evidence of him stalking Maya. Maya confirms the evidence, including cryptic messages sent to her. The murder weapon is also found in Naren's house. Karan accepts that Naren killed Ajit in a delusional state to protect Maya and Tara.

At the station, a guilt-ridden Maya asks Naren why he took the blame for her. Naren reveals that he had spent 10 years of his life on one of the Millennium Prize Problems, which he solved. However, someone else has reached the solution 46 hours before him. Depressed, he was going to commit suicide. Right then, Maya had knocked on Naren's door, giving him a new lease on life. A grateful Maya offers to visit him in prison but Naren refuses, wanting her and Tara to move on in peace.

In a flashback, it shows how Naren covered up the murder. Since Ajit's murder occurred on the 9th and Maya did not have an alibi for then, he killed a homeless man on the 10th, a day Maya and Tara had meticulously created an alibi. Karan had previously noted that the burned remains had a smashed face and burned fingerprints to hide Ajit's identity so the body would not be connected to Maya. In reality, it was done to make sure that no one would realize that the dead body was not Ajit's.

Naren is sentenced to 25 years in prison, which he uses to solve another of the Millennium Problems.