The deceased were identified as Priyanka and Rakesh, also 27-year-old, a businessman from Rohtak in Haryana.
Priyanka lived in central Delhi's Baljit Nagar area with her husband Shipu, who works at a private courier company, and have a seven-year-old daughter and a three-year-old son, a senior police official said.
During investigation it emerged that Rakesh was a frequent visitor at Priyanka's residence and Shipu had forbidden his wife from meeting him. Priyanka's husband Shipu and the children knew Rakesh from quite a long time.
Rakesh suddenly pulled out a gun and shot Priyanka on her head from close range, after which he also allegedly shot himself in his head, they said.
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Hearing gunshots, neighbours rushed to Priyanka's residence and found the two bodies lying in a pool of blood, the official said.
"One of the neighbours called up the police control room and a team was rushed to the spot. Priyanka and Rakesh, whose identity was ascertained with the help of documents in his pocket, were both rushed to a hospital, where they were declared dead," DCP (Central) Parmaditya said.
He added that from preliminary investigation it is clear that Rakesh and Priyanka were close to each other, for she did not resist to his entry in the house today, and Shipu suspected that they had an affair.
"A case has been registered at the Patel Nagar Police Station and the bodies have been sent for a postmortem and investigation is underway," Parmaditya added.