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.

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.