Boats and Streams - Formulas, Tricks, Questions and Solved Examples - Quantitative Aptitude Quiz

Formulas and Quick Tricks for Boats and Streams

  1. Upstream: In water, the direction against the stream is called upstream.
  2. Downstream: In water, the direction along the stream is called downstream.
  3. Let the speed of a boat in still water be u km/hr and the speed of the stream be v km/hr, then:
    • Speed downstream = (u + v) km/hr
    • Speed upstream = (u - v) km/hr.
  4. Let the speed downstream be a km/hr and the speed upstream be b km/hr, then:
    • Speed in still water =1/2(a+b) km/hr
    • Rate of stream = 1/2(a−b) km/hr
  5. A man can row a boat in still water at x km/hr in a stream flowing at y km/hr. If it takes him t hours to row a place and come back, then the distance between the two places = t(x2−y2) / 2x km
  6. A man takes n times as long to row upstream as to row downstream the river. If the speed of the man is x km/hr and the speed of the stream is y km/hr, then x = y(n+1) / (n−1)

Questions and Solved Examples on Boats and Streams

  1. A boat takes 28 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 6km/hr and the speed of the boat in still water is 9 km/hr, what is the distance between A and B?
    A. 115 kms
    B. 120 kms
    C. 140 kms
    D. 165 kms
  2. B. 120 kms
    Downstream speed = 9+6 = 15
    Upstream speed = 9-6 = 3
    Now total time is 28 hours
    If distance between A and B is d, then distance BC = d/2
    Now distance/speed = time, so
    d/15 + (d/2)/3= 28
    Solve, d = 120 kms
  3. Speed of a man in still water is 5 km/hr and the river is running at 3km/hr. The total time taken to go to a place and come back is 10 hours. What is the distance travelled?
    A. 10 kms
    B. 16 kms
    C. 24 kms
    D. 32 kms
  4. D. 32 kms
    Down speed= 5+3= 8
    Up speed= 5-3=2
    Let distance travelled = X
    (X/8)+(X/2)= 10
    X = 16 kms
    Total distance is 16+16 = 32 kms

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  5. A boat running upstream takes 9 hours 48 minutes to cover a certain distance, while it takes 7 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
    A. 5:2
    B. 7:4
    C. 6:1
    D. 8:3
  6. C. 6:1
    Distance covered upstream in 9 hrs 48 min = Distance covered downstream in 7 hrs
    (X-Y) 49/5 = (X+Y) 7
    X/Y = 1/6
  7. A boat can travel 20 km downstream in 24 min. The ratio of the speed of the boat in still water to the speed of the stream is 4 : 1. How much time will the boat take to cover 15 km upstream?
    A. 20 mins
    B. 22 mins
    C. 25 mins
    D. 30 mins
  8. D. 30 mins
    Down speed =20/24*60=50km/hr
    4:1 =4x:x
    Downstream speed = 4x+x=5x
    Upstream speed = 4x-x=3x
    5x= 50; x=10
    so up speed 3*10=30
    Time = 15/30*60= 30 mins
  9. A boat whose speed in 20 km/hr in still water goes 40 km downstream and comes back in a total of 5 hours. The approx. speed of the stream (in km/hr) is:
    A. 6 km/hr
    B. 9 km/hr
    C. 12 km/hr
    D. 16 km/hr
  10. B. 9 km/hr
    Let the speed of the stream be x km/hr. Then,
    Speed downstream = (20 + x) km/hr,
    Speed upstream = (20 – x) km/hr.
    40/20+x + 40/20-x = 5
    X = 9 km/hr appx.
  11. A boat covers a certain distance downstream in 2 hour, while it comes back in 2 1/2 hours. If the speed of the stream be 5 kmph, what is the speed of the boat in still water?
    A. 40 kmph
    B. 30 kmph
    C. 35 kmph
    D. 45 kmph
  12. D. 45 kmph
    Let the speed of the boat in still water be x kmph. Then,
    Speed downstream = (x + 5) kmph,
    Speed upstream = (x – 5) kmph.
    (x + 5)*2 = (x – 5)*5/2
    X = 45 kmph
  13. A boat running downstream covers a distance of 40 km in 5 hrs and for covering the same distance upstream it takes 10 hrs. What is the speed of the stream?
    A. 5 km/hr
    B. 2 km/hr
    C. 6 km/hr
    D. 4 km/hr
  14. B. 2 km/hr
    Downstream speed = 40/5 = 8 km/hr
    Upstream speed = 40/10 = 4 km/hr
    So speed of stream = 1/2*(8-4)
  15. A boat goes 4 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 15 km in stationary water?
    A. 2 hours
    B. 2 hours 15 mins
    C. 3 hours
    D. 3 hours 30 mins
  16. C. 3 hours
    Rate downstream = 1/10 * 60 = 6kmph
    Rate upstream = 4 km/hr.
    Speed in still water = ½ * 10 = 5 kmph
    Required time = 15/5 = 3 hours
  17. A man rows to a place 40 km distant and come back in 9 hours. He finds that he can row 5 km with the stream in the same time as 4 km against the stream. The rate of the stream is:
    A. 1 km/hr
    B. 1.5 km/hr
    C. 2 km/hr
    D. 2.5 km/hr
  18. A. 1 km/hr
    Speed downstream = 5/x
    Speed upstream = 4/x
    40/(5/x) + 40/(4/x) = 9
    X = ½
    So, Speed downstream = 10 km/hr, Speed upstream = 8 km/hr
    Rate of the stream = 1/2 * 2 = 1 km/hr
  19. A man can row 8 km/hr in still water. When the river is running at 4 km/hr, it takes him 2 1/3hr to row to a place and come back. How far is the place?
    A. 4 kms
    B. 5 kms
    C. 7 kms
    D. 10 kms
  20. C. 7 kms
    Downstream speed = 8+4= 12 => a
    Upstream speed = 8-4= 4 => b
    Distance = a*b/(a+b) * total time (t)
    = 12*4/16 * 7/3
    = 7 kms