Usha was killed on the intervening night of November 11 and 12 by her brother-in-law Diwan Singh (20) at her residence in Okhla Industrial Area.
She was first hit with an iron pipe and then strangulated, police said.
Diwan, who has now been arrested, initially attempted to mislead the investigation by terming it as a suicide
However, during interrogation, Diwan confessed he had an "illicit relationship" with Usha and that he killed her as he feared he would be exposed, police said.
He told interrogators that Usha's husband was an alcoholic and was under treatment at a De-addiction Centre and during his absence both had developed a relationship.
One day Usha informed Diwan that she was pregnant. Diwan panicked and decided to eliminate her.
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