Question
Calculate the total time it takes for a ship to cover a
distance of 120 km downstream and 80 km upstream. Statement I: The ship can travel 1300 km in 13 hours, with 40% of the distance covered upstream. Statement II: The ship's speed in still water is 50% greater than the speed of the stream. Statement III: The ship can travel 650 km downstream in 2.5 hours, which is the same amount of time it takes to travel 130 km upstream. Statement IV: Both the downstream and upstream speeds of the ship are multiples of 13. The question presents four statements, labeled as "I, II, III, and IV." determine which of these statements, contains sufficient data to answer the questio n. .Solution
We can say that Statement I: Distance travelled by the ship in downstream = 0.6 × 1300 = 780 km Distance travelled by the ship in upstream = 1300 – 780 = 520 km time taken by ship to travel (780 km downstream + 520 km upstream) = 13 hours Time taken by ship to travel 6.5 × (120 km downstream + 80 km upstream) = 13 Time taken by the ship to travel (120 km downstream + 80 km upstream) = 13/6.5 = 2 hours So, data in statement I alone is sufficient to answer the question Statement II: Let the speed of the stream be ‘s’ km/hr Therefore, speed of ship in still water = 1.5s km/hr We cannot determine the required time. So, data in statement II alone is not sufficient to answer the question. Statement III: ATQ, Downstream speed of the ship = 650/2.5 = 260 km/hr Upstream speed of the ship = 130/2.5 = 52 km/hr Therefore, required time taken = {(120/260) + (90/52)} ~ 0.5 + 1.5 ~ 2 hours So, data in statement III alone is sufficient to answer the question. Statement IV: We cannot determine the required time. So, data in statement IV alone is not sufficient to answer the question.
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