Um, this question doesn't make sense because New Delhi and Delhi are actually one city. The city New Delhi was changed back to Delhi recently. There is no difference between the two...
A random search for flights from Delhi (DEL) to Cape Town (CPT) shows:
OPTION 1: 15hr 30min via Dubai (DXB)
DEL - DXB Emirates Airlines Flt 513 Dep 04:15am 14Jan,Thu
DXB - CPT Emirates Airlines...
It takes about anywhere from 30-45 minutes from West Delhi to India Gandhi Airport depending where you are. It could be more during morning hours or early evening hours.