Question
Speed of a boat in still water is 20 km/h while the
speed of stream is ____ km/h. Total time taken by the boat to go 200 km upstream and 300 km downstream is ____ hours. The values given in which of the following options will fill the blanks in the same order in which it is given to make the above statement true: I. 7, 26.67 II. 8, 25 III. 9, 27.5 IV. 10, 30Solution
For I: Speed of boat = 20 km/h Speed of stream = 7 km/h Speed in upstream = 20 – 7 = 13 km/h Speed in downstream = 20 + 7 = 27 km/h Total time = 200/13 + 300/27 = 15.38 + 11.11 = 26.49 hours So, I can be the answer. For II: Speed of boat = 20 km/h Speed of stream = 8 km/h Speed in upstream = 20 – 8 = 12 km/h Speed in downstream = 20 + 8 = 28 km/h Total time = 200/12 + 300/28 = 16.67 + 10.71 = 27.38 hours So, II can’t be the answer. For III: Speed of boat = 20 km/h Speed of stream = 9 km/h Speed in upstream = 20 – 9 = 11 km/h Speed in downstream = 20 + 9 = 29 km/h Total time = 200/11 + 300/29 = 18.18 + 10.34 = 28.52 hours So, III can’t be the answer. For IV: Speed of boat = 20 km/h Speed of stream = 10 km/h Speed in upstream = 20 – 10 = 10 km/h Speed in downstream = 20 + 10 = 30 km/h Total time = 200/10 + 300/30 = 20 + 10 = 30 hours So, IV can be the answer.
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