The 30-year-old woman has been hospitalised and is in a critical condition, they said.
Ajay, who used to work as a labourer, had been in love with the woman for the past three-four months, police said.
Police said the woman's husband had asked both of them to not meet or talk but Ajay kept coming to their home in Ghazipur.
Today, Ajay came to the woman's house at around 11.30 am when her husband and five-year-old child were away. They had an argument and in a fit of rage, he strangulated her and later hanged himself, said DCP (East) Rishi Pal Singh.
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The woman's brother has alleged Ajay tried to kill his sister, added the officer.
The woman wanted to end the relationship since there was pressure from her family but Ajay wasn't listening, police said. However, since the woman is in a critical condition, the police doesn't know the exact cause of their argument.
The woman is admitted to Lal Bahadur Shastri Hospital and her condition is stated to be critical, added the officer.
A case under section 307 IPC (attempt to murder) has been registered at Ghazipur police station and further investigation is underway.
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