Question
The time taken by Boat 'X' to travel a distance of '2a'
km upstream is the same as the time it takes to travel '3a' km downstream. Similarly, the time taken by Boat 'Y' to cover '3b' km upstream equals the time to cover '5b' km downstream, and the time taken by Boat 'Z' to cover '5c' km upstream matches the time to cover '7c' km downstream. Quantity I: Boat 'X' travels 144 km downstream and then returns to the starting point in a total of 20 hours. Find the speed of Boat 'X' in still water. Quantity II: Boat 'Y' travels 150 km downstream and then returns to the starting point in a total of 16 hours. Determine the speed of Boat 'Y' in still water. Quantity III: Boat Z travels 140 km downstream and then returns to the starting point in a total of 12 hours. Calculate the speed of Boat 'Z' in still water. In the question, three quantities i.e. Quantity I, Quantity II and Quantity III are given. Solve the given quantities to establish the correct relation between them and choose the correct option.Solution
ATQ, For Boat X, Downstream Speed : Upstream Speed = 3a : 2a = 3 : 2 For Boat Y, Downstream Speed : Upstream Speed = 5b : 3b = 5 : 3 For Boat Z, Downstream Speed : Upstream Speed = 7c : 5c = 7 : 5 Quantity I, For Boat 'X', Downstream Speed = 3p km/hr Upstream Speed = 2p km/hr 144/3p + 144/2p = 20 48/p + 72/p = 20 120/p = 20 p = 6 Speed of Boat 'X' in still water = (3p + 2p)/2 = 5p/2 = 2.5 Ă— 6 = 15 km/hr Quantity II, For Boat 'Y', Downstream Speed = 5q km/hr Upstream Speed = 3q km/hr 150/5q + 150/3q = 16 30/q + 50/q = 16 80/q = 16 q = 5 Speed of Boat 'Y' in still water = (5q + 3q)/2 = 8q/2 = 4 Ă— 5 = 20 km/hr Quantity III, For Boat Z, Downstream Speed = 7r km/hr Upstream Speed = 5r km/hr 140/7r + 140/5r = 12 20/r + 28/r = 12 48/r = 12 r = 4 Speed of Boat Z in still water = (7r + 5r)/2 = 12r/2 = 6 Ă— 4 = 24 km/hr Quantity I < Quantity II < Quantity III
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