Boats and Streams

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  1. A man can row 71/2 km/h in still water. If in a river running at 1.5 km/h, it takes him 50 min to row to a place and back, how far off is the place ?








  1. View Hint View Answer Discuss in Forum

    Let the distance be L km.
    Speed of the main in still water = 71/2 km/h
    and speed of the river = 15 km/h

    ∴ Speed of the man downstream = 7.5 + 1.5 = 9
    Speed of the man upstream = 7.5 - 1.5 = 6 km/h

    According to the question,
    L/9 + L/6 = 50/60

    Correct Option: A

    Let the distance be L km.
    Speed of the main in still water = 71/2 km/h
    and speed of the river = 15 km/h

    ∴ Speed of the man downstream = 7.5 + 1.5 = 9
    Speed of the man upstream = 7.5 - 1.5 = 6 km/h

    According to the question,
    L/9 + L/6 = 50/60
    ⇒ (4L + 6L)/36 = 50/60
    ⇒ 10L/36 = 50/60
    ⇒ L = (50 x 36)/(10 x 60)
    5⇒ x = 3 km

  1. Ishwar is rowing a boat. He takes half time in moving a certain distance downstream than upstream. What is the ratio of the rate of boat in still water to the rate of current ?








  1. View Hint View Answer Discuss in Forum

    Let speed of Ishwar's boat in still water be x km/h
    and speed of current = y km/h
    Rate downstream = (x + y) km/h
    Rate upstream = (x - y) km/h
    Let the distance covered in each case be a.
    According to the question,
    2a/(x + y) = a/(x - y)

    Correct Option: D

    Let speed of Ishwar's boat in still water be x km/h
    and speed of current = y km/h
    Rate downstream = (x + y) km/h
    Rate upstream = (x - y) km/h
    Let the distance covered in each case be a.
    According to the question,
    2a/(x + y) = a/(x - y)
    ⇒ 2(x - y) = x + y
    2x - 2y = x + y
    ⇒ x = 3y
    ∴ x/y = 3/1
    ⇒ x : y = 3 : 1

  1. A river is flowing at a speed of 5 km/h in a particular direction. A man, who can swim at a speed of 20 km/h in still water, starts swimming along the direction of flow of the river from from points A and reaches another point B which is at a distance of 30 km from the starting point A. On reaching point B, the man turns back and starts swimming against the direction of flow of the river and stops after reaching point A. The total time taken by the man to complete his journey is ?








  1. View Hint View Answer Discuss in Forum

    Given,
    Speed of the stream = 5 km/h
    and speed of the man in still water = 20 km/h
    ∴ Speed of the man downstream = 20 + 5 = 25 km/h
    and speed of the man upstream = 20 - 5 = 15 km/h
    ∴ Total time taken to complete the whole journey = 30/25 + 30/15

    Correct Option: B

    Given,
    Speed of the stream = 5 km/h
    and speed of the man in still water = 20 km/h
    ∴ Speed of the man downstream = 20 + 5 = 25 km/h
    and speed of the man upstream = 20 - 5 = 15 km/h
    ∴ Total time taken to complete the whole journey = 30/25 + 30/15
    = (30 x 8) / 75
    = 3 h 12 min

  1. A river is flowing with a steady speed of 4 km/h. One rows his boat downstream in the river and then returns by rowing upstream in the same river. When he returns to the starting points, the total distance covered by him is 42 km. If the return journey takes 2 h more than his outward journey, then the speed of his rowing in still water must be ?








  1. View Hint View Answer Discuss in Forum

    Let the speed of rowing in still water be u km/h.
    Distance in downstream motion = 21 km
    and speed downstream = (u + 4) km/h
    ∴ Time taken = 21/ (u + 4)
    Distance upstream motion = 21 km and speed upstream = (u +4) km
    ∴ Time taken = 21/(u - 4)

    According to the question.
    21/(u + 4) + 2 = 21/(u - 4)

    Correct Option: B

    Let the speed of rowing in still water be u km/h.
    Distance in downstream motion = 21 km
    and speed downstream = (u + 4) km/h
    ∴ Time taken = 21/ (u + 4)
    Distance upstream motion = 21 km and speed upstream = (u +4) km
    ∴ Time taken = 21/(u - 4)

    According to the question.
    21/(u + 4) + 2 = 21/(u - 4)
    ⇒ (21 + 2u + 8)/u + 4 = 21/(u - 4)
    ⇒ (2u + 29)/(u + 4) = 21/(u - 4)
    ⇒ (u - 4) (2u + 29) = 21(u + 4)
    ⇒ 2u2 - 8u + 29u - 116 = 21u + 84
    ⇒ 2u2 + 21u - 116 = 21u + 84
    ⇒ 2u2 = 84 + 116
    ⇒ u2 = 200/2
    ⇒ u2 = 100
    ⇒ u = 10 km/h

  1. A boatman takes twice as long to row a distance against the stream as to row the same distance with the stream. Find the ratio of speeds of the boat in still water and the stream. ?








  1. View Hint View Answer Discuss in Forum

    Let boatman's speed upstream x
    And his speed downstream = 2x
    ∴ Ratio = (Speed in still water) : (Speed of stream)

    Correct Option: B

    Let boatman's speed upstream x
    And his speed downstream = 2x
    ∴ Ratio = (Speed in still water) : (Speed of stream)
    = (2x + x/2) : (2x - x/2)
    = 3x/2 : x/2
    = 3 : 1