Boats and Streams – Aptitude Questions and Answers

Boats and Streams Questions and Answers

The subject matter of Boats and Streams Questions is quite essential as these questions are there in nearly all competitive exams from the topic. On this page we will discuss about Questions asked About the topic boats and streams.

Boats and Streams Questions

Rules:

  • When the speed of the boat or swimmer is ‘x’ km per hour and the stream’s speed is ‘y’ km per hour, then:
    • The speed of the swimmer or boat upstream = (x – y) km per hour
    • The speed of the swimmer or boat downstream = (x + y) km per hour
  • In the stationary or still water
    • The speed of the boat is given by = 1/2 (downstream speed + upstream speed)
    • The speed of the stream is provided by = 1/2 (downstream speed – upstream speed)
  • A certain distance in p1 hours is covered by a man when he rows downstream and comes back the equal distance upstream in p2 hours. If the stream’s speed is assumed as s km/hr, then the man’s speed in still water will be:
     s = ( p2+ p1)/ ( p2-p1)km/hr 

             where , 

                  s = speed of man.
                 p2 = time taken to cover upstream
                 p1 = time taken to cover downstream

Boats and Streams Formulas

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1. Alex can row a boat at 7 kmph downstream and 3 kmph upstream. Calculate her rowing speed in still water and the rate of the current?

5 Kmph and 2 kmph

5 Kmph and 2 kmph

87.05%

7.5 kmph and 3 Kmph

7.5 kmph and 3 Kmph

4.97%

6.4 kmph and 14 kmph

6.4 kmph and 14 kmph

2.86%

None of the above

None of the above

5.12%

Rowing speed of Alex in still water=  (Rate upstream+ Rate Downstream)

= \frac{7 + 3}{2}= 5 kmph

And rate of the current= \frac{7 - 3}{2}= 2 kmph

2. Sam’s Rowing speed is 10 kmph, but he takes double time in rowing the boat upstream in comparison to downstream. Calculate the rate of the stream?

2.18 kmph

2.18 kmph

10.77%

3.33 kmph

3.33 kmph

69.51%

1.56 kmph

1.56 kmph

7.52%

4.36 kmph

4.36 kmph

12.2%

Since it is mentioned that his speed downstream is twice that of the upstream.

So let Sam’s speed upstream be ‘a’ then his speed downstream= 2a

Therefore  \frac{2a + a}{2}= 10 or a= 6.66 kmph

Hence his speed upstream= 6.66 kmph and

His speed downstream= 6.66*2= 13.33 kmph

Therefore the rate of the current= 3.33 kmph

3. What will be the speed of the boat if the river flows at a speed of 2 km/hr, and it takes 12 minutes to cover 4 km upstream?

21

21

6.03%

16

16

18.09%

22

22

69.44%

30

30

6.44%

Speed upstream = \frac{4}{\frac{12}{60}}= 20 km/hr
Speed of the stream = 2 km/hr
Speed of boat in still water = (20+2) = 22 km/hr

4. Calculate the speed of a motorboat in still water if current of the river flows at 2 kmph, and the boat takes 40 mins. To cover 10 km upstream and back again at the starting point.

19

19

14.01%

30.13

30.13

51.54%

26

26

13.17%

None

None

21.29%

Let the speed of the boat be ‘a’ (in still water)

Therefore speed downstream= a+2

And speed upstream= a-2

Time taken to cover 10 km back and forth= \frac{10}{a+2} + \frac{10}{a-2}= 40/60

= a2-30a-4= 0

Solving the above equation we get a = 30.13

5. Sam rows a boat at a speed of 6 kmph in still water. If the speed of the stream 2 kmph, in how much time will Sam take to cover 36 km downstream?

7

7

5.36%

4.5

4.5

83.65%

6.2

6.2

5.36%

3

3

5.63%

Speed of the boat with the stream= 6+2= 8 kmph

Therefore time taken by Sam to Cover 36 km= \frac{36}{8}= 4.5 hours

6. Tom takes 2 hours to sail a boat for 4 km against the stream and can cover 2 km distance in 20 minutes if he rows the boat along with the current of the river. Calculate the time taken to cover 10 km in stagnant water?

2.5

2.5

72.35%

3.3

3.3

10.59%

4.7

4.7

7.35%

None

None

9.71%

Speed Downstream= 2/20 * 60 = 6 kmph

Speed Upstream= 4/2= 2 kmph

Speed in stable water= \frac{6 + 2}{2}= 4 kmph

Hence time taken t cover 10 km= 10/4 =  2.5 hrs

7. Sam takes 12.5 minutes to cover 900 meters distance rowing the boat against the stream of the river and takes 7.5 minutes to row the same boat downstream. Calculate Sam’s speed of rowing the boat in still water?

5.76 kmph

5.76 kmph

62.73%

4.75 kmph

4.75 kmph

13.28%

2.65 kmph

2.65 kmph

13.28%

3.22 kmph

3.22 kmph

10.7%

Let the speed of the boat in still water be

Sam takes 12.5 minutes 750 seconds to cover 900 m upstream

Therefore speed upstream= 900/750 = 1.2 mps

As the time taken downstream 7.5 min or 450 sec

Therefore speed downstream = 900/450= 2 mps

Therefore speed in stable water= 1/2 * (1.2+2)= 1.6 mps

Or 1.6* (3600/1000) = 1.6 * 18/5= 5.76 kmph

8. The speed of a boat in still water is 4.5 kmph, and the rate of the river flow is 3 kmph. Calculate the total time taken by Agatha to cover a distance of 7.5 km to and fro in the same river?

6 hrs

6 hrs

70.99%

5 hrs

5 hrs

12.21%

4 hrs

4 hrs

10.69%

5.5 hrs

5.5 hrs

6.11%

Speed of the boat upstream= 4.5-3= 1.5 kmph

Speed of the boat downstream= 4.5+3= 7.5 kmph

Therefore total time taken=\frac{7.5}{1.5} + \frac{7.5}{7.5}= 5 + 1 = 6 hrs

9. Sam takes triple time to row a boat against the stream of the river than the time he takes to row with the stream to cover the same distance. What will be the ratio between the speed of the boat in still water to that of the flow?

3:2

3:2

10%

2:1

2:1

63.7%

3:1

3:1

21.48%

4:3

4:3

4.81%

Let Sam’s speed upstream be a kmph

Speed downstream= 3a kmph

Therefore the speed of the boat in still water: Speed of river stream

= \frac{3a +a}{2}:\frac{3a - a}{2}

\frac{4a}{2}:\frac{2a}{2}Or 2: 1

10. Alex can row a boat in still water at a speed of 5 km/h. He rows the boat upstream for 2 hours and covers a distance of 10 km. Then, he rows downstream for 1.5 hours and covers a distance of 12 km. Calculate the speed of the stream.

2/7

2/7

7.51%

1.5

1.5

81.03%

1.4

1.4

6.32%

4

4

5.14%

Given: Speed of Boat in Still Water = 5 km/h Time taken upstream = 2 hours Distance upstream = 10 km Time taken downstream = 1.5 hours Distance downstream = 12 km

First, let's calculate the speed of the boat in the upstream and downstream directions:

Speed Upstream = Distance Upstream / Time Upstream Speed Upstream = 10 km / 2 hours Speed Upstream = 5 km/h

Speed Downstream = Distance Downstream / Time Downstream Speed Downstream = 12 km / 1.5 hours Speed Downstream = 8 km/h

Now, use the formula to calculate the speed of the stream:

Speed of Stream = (Speed Downstream - Speed Upstream) / 2 Speed of Stream = (8 km/h - 5 km/h) / 2 Speed of Stream = 3 km/h / 2 Speed of Stream = 1.5 km/h

So, the speed of the stream is 1.5 km/h.

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