Question
Find and compare the speeds of
the boats in still water based on the given conditions. Boat A takes the same amount of time to travel 2x km upstream as it does to travel 3x km downstream. Boat B takes the same amount of time to travel 3y km upstream as it does to travel 5y km downstream. Boat C takes the same amount of time to travel 5z km upstream as it does to travel 7z km downstream. Quantity I: Boat A covers 144 km downstream and then returns to the starting point, completing the round trip in 20 hours. Find the speed of Boat A in still water. Quantity II: Boat B covers 150 km downstream and returns to the starting point, completing the round trip in 16 hours. Find the speed of Boat B in still water. Quantity III: Boat C covers 140 km downstream and returns to the starting point, completing the round trip in 12 hours. Find the speed of Boat C 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 optionSolution
ATQ, For Boat A, Downstream Speed : Upstream Speed = 3x : 2x = 3 : 2 For Boat B, Downstream Speed : Upstream Speed = 5y : 3y = 5 : 3 For Boat C, Downstream Speed : Upstream Speed = 7z : 5z = 7 : 5 Quantity I, For Boat A, Downstream Speed = 3a km/hr Upstream Speed = 2a km/hr 144/3a + 144/2a = 20 48/a + 72/a = 20 120/a = 20 a = 6 Speed of Boat A in still water = (3a + 2a)/2 = 5a/2 = 2.5 × 6 = 15 km/hr Quantity II, For Boat B, Downstream Speed = 5b km/hr Upstream Speed = 3b km/hr 150/5b + 150/3b = 16 30/b + 50/b = 16 80/b = 16 b = 5 Speed of Boat b in still water = (5b + 3b)/2 = 8b/2 = 4 × 5 = 20 km/hr Quantity III, For Boat C, Downstream Speed = 7c km/hr Upstream Speed = 5c km/hr 140/7c + 140/5c = 12 20/c + 28/c = 12 48/c = 12 c = 4 Speed of Boat C in still water = (7c + 5c)/2 = 12c/2 = 6 × 4 = 24 km/hr Quantity I < Quantity II < Quantity III
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