A boat travels 63 km downstream in T hours and 54 km upstream in 2T hours. It also travels 70 km downstream and 60 km upstream in 6 hours. Find the time taken by the boat to travel 275 km in still water.

ATQ, Let downstream speed be D km/hr and upstream speed be U km/hr. Time taken to cover 63 km downstream = T hours. So, T = 63/D. Time taken to cover 54 km upstream = 2T hours. So, 2T = 54/U. Put T = 63/D in the second relation. 2 × 63/D = 54/U. 126/D = 54/U. 126U = 54D. D/U = 126/54 = 7/3. So, downstream speed : upstream speed = 7 : 3. Let downstream speed = 7x and upstream speed = 3x. The boat covers 70 km downstream and 60 km upstream in 6 hours. So, 70/7x + 60/3x = 6. 10/x + 20/x = 6. 30/x = 6. x = 30/6 = 5. Downstream speed = 7 × 5 = 35 km/hr. Upstream speed = 3 × 5 = 15 km/hr. Speed in still water = (Downstream speed + Upstream speed)/2. Speed in still water = (35 + 15)/2 = 50/2 = 25 km/hr. Time taken to cover 275 km in still water = 275/25 = 11 hours.