The speed of Boat in still water is 35Km/h and speed of the stream is 15km/h. The distance between Gomatinagar and Ghazipur is 800km. The boat started travelling in downstream from Gomatinagar to Ghazipur and in the midway, it is powered by an engine due to which the speed of boat increased. Now boat reached Ghazipur and starts back to Gomatinagar with help of the same engine. Total time taken in entire journey is 29 hours. Then find the increment in speed of boat due to this engine.

Let's denote the boat's still water speed as b=35 km/h and stream speed as s=15 km/h. Normal downstream speed = b+s = 50 km/h, normal upstream speed = b-s = 20 km/h. With engine, let the increased speed be e km/h, so downstream with engine = 50+e, upstream with engine = 20+e. Total distance = 800+800 = 1600 km. Half downstream (400 km) at 50 km/h takes 8 hours, remaining 400 km with engine at (50+e) km/h takes 400/(50+e) hours. Entire upstream (800 km) with engine at (20+e) km/h takes 800/(20+e) hours. Total time = 8 + 400/(50+e) + 800/(20+e) = 29. Solving: 400/(50+e) + 800/(20+e) = 21. Testing e=30: 400/80 + 800/50 = 5 + 16 = 21. ✓ The increment is 30 km/h.