A minimum of one business week (5 working days/7 normal days). It can take a few days additionally depending on where you live and which consulate general's office your passport went to, for stamping (New Delhi/Chandigarh/Bengaluru/Mumbai).
Where you live in your city may also matter. If you do not live close to a bluedart hub, or live in the outskirts, or live in a tier-II or tier-III city, the time it takes for the passport to reach the bluedart hub and then the local hub, and then for the bluedart executive to deliver it to your door, can change.
There are a multitude of factors at play here.