The decomposed bodies of a family of four were found in their apartment in the North 24 Parganas district of West Bengal on Sunday, the police said.
The police suspect that the man, identified as Brindaban Karmakar, 52, killed his family by poisoning them and then died by suicide.
The police went to the house in Khardah after neighbours complained of a foul smell from the apartment. They broke open the door and found the four bodies.
While Mr Karmakar's body was found hanging from the ceiling, the bodies of his wife Debasree, 17-year-old daughter Debaleena, and eight-year-old son Utsaha were found in different places in the flat, the police said.
A suicide note was found, the police said, in which Mr Karmakar claimed his wife had an extra-marital affair and he could not bear it.
A local Trinamool Congress leader said that the man who operates the water pump in the building went to Mr Karmakar's flat on Sunday morning for a bunch of keys but got no response.
"He kept ringing the doorbell but nobody answered. He also noticed a stench and informed the local councillor who alerted the police. Police broke open the door and found the four bodies," he said.
"It is difficult to know the reason behind this," he said, adding that the man met them the day after Kali Pujo.
"This incident has shocked people of the neighbourhood," he said.
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