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. Answer: B. 120 kms
    Explanation:
    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. Answer: D. 32 kms
    Explanation:
    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. Answer: C. 6:1
    Explanation:
    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. Answer: D. 30 mins
    Explanation:
    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. Answer: B. 9 km/hr
    Explanation:
    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. Answer: D. 45 kmph
    Explanation:
    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. Answer: B. 2 km/hr
    Explanation:
    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. Answer: C. 3 hours
    Explanation:
    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. Answer: A. 1 km/hr
    Explanation:
    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. Answer: C. 7 kms
    Explanation:
    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