The duo had gone to the woman's house to rob her and had fled with jewellery and some cash, they said.
Two gold bangles and Rs 28,000, that were stolen from the victim's house, have been recovered from them, police said.
Sangeeta Bansal was found dead in her apartment with stab injuries on her neck and abdomen yesterday.
They duo has been identified as Rakesh and Mukesh.
During interrogation, they said they had taken a loan of Rs 50,000 from the woman and could not pay it back. They had also kept some jewellery with her as a security which she had refused to return until they paid her the money, police said.
Police said when they entered the house, Bansal was talking to a relative over the phone and had told them to wait. However, they insisted that she disconnect the call and speak to them.
Bansal had left her phone on the call mode with the relative, on the table when the two got into an argument with her. The relative, on the other end of the phone, heard their names several times, before they killed Bansal.
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