Question
The sum of the speeds of two boats A and B in still
water is 56 km/hr. such that the speed of boat A in still water is 25% less than that of boat B in still water. If the upstream speed of boat A is 88% less than the downstream speed of boat B, then find the speed of the current.Solution
Let the speed of boat B in still water be x km/hr. Therefore, the speed of boat A in still water =0.75x km/hr. According to the question, 0.75x + x = 70 Or, 1.75x = 70 Or x = 40 Therefore, the speed of boat B in still water = x =40 km/hr. Speed of boat A in still water = 0.75x = .75×40=30km/hr. Let the speed of the current be ‘y’ km/hr. Downstream speed of boat B = (40 + y) km/hr. Upstream speed of boat A = (30 – y) km/hr. 0.12(40 + y) = 30 – y Or, 4.8 + 0.12y = 30 – y Or, 0.12y + y = 30 – 4.8 1.12y =25.2 y=25.2/1.12=22.5 therefore, speed of the current =22.5km/hr.
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