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(34.Amotor boat covers a certain distance downstream in a river in five hours. It covers thesame distance upstream in five hours and a half. The speed of the water is 1.5 km/hr.The speed of the boat in still water is(A) 30 km/hr (B) 30.5 km/hr (C) 31.5 km/hr (D) 20 km/hr |
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Answer» option C is the correct answer Let the speed of boat in still water = x km/hspeed of water = 1.5 km/h Speed of boat downstream = (x+1.5) km/htime taken in downstream journey = 5 hoursdistance travelled = 5(x+1.5) km Speed of boat upstream = (x-1.5) km/htime taken in downstream journey = 5.5 hoursdistance travelled = 5.5(x-1.5) km Since same distance is covered in both the cases 5(x+1.5) = 5.5(x-1.5)⇒ 5x + 5×1.5 = 5.5x - 5.5×1.5⇒ 5x + 7.5 = 5.5x - 8.25⇒ 5x - 5.5x = -8.25 - 7.5⇒ -0.5x = -15.75⇒ x = (-15.75)/(-0.5)⇒ x = 31.5 km/h Hence speed of boat in still water is 31.5 km/h. |
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