Multiple choice

A fisherman sails his boat along the stream from X to Y, which is 36 km far. Also, it is known that the times taken by him to cover 6 km downstream and 4 km upstream are the same. If the time taken by him to go to point Y and return to point X is 6 hours, then what is the speed of flow of water in the river?

  1. 2.25 km/hr

  2. 2.50 km/hr

  3. 2.75 km/hr

  4. 3.25 km/hr

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let speed of boat be b and stream be s. Downstream speed is b+s, upstream is b-s. 6/(b+s) = 4/(b-s) implies 6b-6s = 4b+4s, so 2b = 10s or b = 5s. Total time for 36 km round trip is 36/(b+s) + 36/(b-s) = 6. Substituting b=5s: 36/(6s) + 36/(4s) = 6, so 6/s + 9/s = 6, 15/s = 6, s = 2.5 km/hr.

AI explanation

Let the downstream speed be U and the upstream speed be V. Since the time taken to cover 6 km downstream and 4 km upstream is the same, 6 / U = 4 / V, which gives U / V = 3 / 2. The speed of the boat in still water is 5 units and the speed of the stream is 1 unit. The total time for the 36 km round trip is (36 / (6x)) + (36 / (4x)) = 15 / x = 6 hours, so x = 2.5 km/hr. The result is 2.50 km/hr.

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