Question
What is the time taken by the boat to travel 48 km in
still water? Statement I: Â The boat travels 36 km upstream and 60 km downstream in 6 hours. Statement II: Â The upstream speed of the boat is 40% slower than its downstream speed. Statement III: Â The boat travels 30 km upstream and 70 km downstream in 6 hours. The problem presents three statements labeled as "I, II, and III," and you need to determine whether the data provided in these statements is sufficient to answer the question.Solution
ATQ, Statement I: Let the downstream and upstream speeds of the boat are 'x' km/h and 'y' km/h respectively. So, 60/x + 36/y = 6 Here we have two variables, so the equation can’t be solved. Data in statement I alone is not sufficient to answer the question. Statement II: Let the downstream speed of the boat = x km/h So the upstream speed of the boat = 0.6x km/h No additional data is given, so the speed of the boat can’t be determined. Data in statement II alone is not sufficient to answer the question. Let the downstream and upstream speeds of the boat are x km/h and y km/h respectively. So 70/x + 30/y = 6 Here we have two variables, so the equation can’t be solved. Data in statement III alone is not sufficient to answer the question. Combining statements I and II: Let the downstream speed of the boat = x km/h So the upstream speed of the boat = 0.6x km/h 60/x + 36/0.6x = 6 60/x + 60/x = 6 x = 120/6 = 20 So the downstream and upstream speeds of the boat are 20 km/h and 12 km/h respectively. Speed of the boat in still water = (20 + 12)/2 = 16 km/h So the time taken by the boat to cover 48 km in still water = 48/16 = 3 hours Data in statements I and II together are necessary to answer the question. Combining statements II and III: Let the downstream speed of the boat = x km/h So the upstream speed of the boat = 0.6x km/h 70/x + 30/0.6x = 6 70/x + 50/x = 6 x = 120/6 = 20 So the downstream and upstream speeds of the boat are 20 km/h and 12 km/h respectively. Speed of the boat in still water = (20 + 12)/2 = 16 km/h So the time taken by the boat to cover 48 km in still water = 48/16 = 3 hours Data in statements II and III together are necessary to answer the question. Combining statements I and III: Let the downstream and upstream speeds of the boat are x km/h and y km/h 60/x + 36/y = 6 ………. (i) 70/x + 30/y = 6 ………. (ii) Solving equations (i) and (ii), we get x = 20 and y = 12 So the downstream and upstream speeds of the boat are 20 km/h and 12 km/h respectively. Speed of the boat in still water = (20 + 12)/2 = 16 km/h So the time taken by the boat to cover 48 km in still water = 48/16 = 3 hours Data in statements I and III together are necessary to answer the question.
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