The ratio of the time taken by a boat to cover D km downstream to the time taken to cover (D/2 + 4) km upstream is 1 : 3. The ratio of the downstream speed of the boat to its speed in still water is 5 : 3. If the difference between the time taken to cover (D − 10) km upstream and the same distance downstream is 3 hours, find the distance covered by the boat in still water in 4 hours.

ATQ, Let the downstream speed of the boat be 5a. Let the speed of the boat in still water be 3a. Speed of the current = 5a − 3a = 2a Upstream speed = 3a − 2a = a Time taken to cover D km downstream = D/5a Time taken to cover (D/2 + 4) km upstream = (D/2 + 4)/a Given ratio of these times = 1 : 3 So, D/5a : (D/2 + 4)/a = 1 : 3 D/5a ÷ (D/2 + 4)/a = 1/3 D/[5(D/2 + 4)] = 1/3 3D = 5(D/2 + 4) 3D = 5D/2 + 20 Multiply both sides by 2. 6D = 5D + 40 6D − 5D = 40 D = 40 Now, D − 10 = 40 − 10 = 30 km Time taken to cover 30 km upstream = 30/a Time taken to cover 30 km downstream = 30/5a Given difference = 3 hours 30/a − 30/5a = 3 30/a − 6/a = 3 24/a = 3 a = 24/3 = 8 Speed in still water = 3a = 3 × 8 = 24 km/hr Distance covered in still water in 4 hours = 24 × 4 = 96 km