Bengaluru (India) and Madanapalle (India) are 118 km (73 mi) apart in a straight line. The way we suggest is by train and bus, via Tirupati and Kalikiri: ~6h door to door with 2 changes. No flight is needed.
Step by step
Train from Bengaluru to Tirupati: ~3h 5m, 211 km
Train from Tirupati to Kalikiri: ~1h 10m, 67 km
Bus from Kalikiri to Madanapalle: about 1h 15m, 34 km
Every route we know
Train + Bus, via Tirupati and Kalikiri: ~6h, 2 changes
Bus, via Chittoor and Kalikiri: ~7h 15m, 2 changes
Flight + Train + Bus, via Chennai, Tirupati and Kalikiri: ~8h 10m, 3 changes
Flight + Train + Bus, via Vijayawada, Tirupati and Kalikiri: ~8h 30m, 3 changes
Bus + Train + Bus, via Chittoor, Tirupati and Kalikiri: ~8h 30m, 3 changes
Times are rough door-to-door times, with time to change and to get through airports included. A "~" marks a rough time worked out from the distance. We don't have timetables, and fares are rough estimates, not quotes: check Google Maps or the operator before you travel.