Arvind Gupta, who was found in possession of the gold jewellery stolen from the victim's house, was nabbed at Howrah railway station and is being brought to Mumbai, they said.
"The accused was preparing to crossover to Bangladesh. He was arrested from the railway station at about 6 AM today," Joint Commissioner of Police (Crime) Sadanand Date said.
The accused has confessed to the crime, he said.
The CCTV footage of the building led the police to Gupta, who worked with a local mobile store, and met the 32-year-old woman at her home regularly, police added.
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The accused slit the throat of Khan, a homemaker, with a knife and stole gold ornaments. As he was about to leave, her two minor daughters entered the house. Gupta tried to attack them with the knife, but the children managed to save themselves.
During investigation it came to light that Gupta has a female friend in Bangladesh, who was in Mumbai sometime back.
"He wanted to go there may be to settle permanently. He murdered Khan to rob her house so that he can have money to reach Bangladesh," Assistant Commissioner of Police Sunil Deshmukh said.
Police suspect Gupta must have visited the adjoining country earlier.
Gupta knew the victim and was possibly aware that Khan had kept jewellery worth lakhs of rupees at her house, police said.