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Boat & Stream | Formulas – Solved Problems, Aptitude Concepts, Imp Questions

Boat & Stream

Boat & Stream is very important topic from the perspective of competitive examinations. Questions are often asked from this topic in SSC, IBPS, POLICE, RAILWAY, and other exams, once its rules are understood then the questions are very easy. It will start to happen, and after a little practice you will be able to solve these problems in your mind.

Also Questions related to Boat And Stream are very easy to understand. Only you have to remember and understand its aptitude concepts. Here the boat and stream related important questions are made available for you. By understanding them through the formulas, you can score great marks in the examinations. To understand this topic better, you must first assimilate the rules and formulas given below.

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Boat & Stream

Boat & Stream Aptitude Concept

What is a Stream?

Running water is called Stream. That is, if the water is flowing in any direction, then we call it a stream.

What Is The Current Speed?

When we steer a boat in the direction in which the stream is going, then that speed is called the current.

What Is A Counter Current Move?

When we move a boat not in the direction of the stream but in the opposite direction from the direction of the stream, then the speed of our boat is called counterclockwise.

What Is A Still Water?

When the speed of water is 0, we call it still water. Under this circumstance the water is considered to be stationary and the speed of the water is zero.

What is Downstream?

If the boat is flowing along the direction of the stream, it is called downstream. In this case, the net speed of the boat is called downstream speed.

What is Upstream?

If the boat is flowing in the opposite direction to the stream, it is called upstream. In this case, the net speed of the boat is called the upstream speed.

Boat & Stream Formulas

1) If the speed of the boat or swimmer is X km/hr and the speed of the stream is Y km/hr,
The speed of the boat or swimmer in the direction of the stream is known as speed downstream. It is given by;

Speed downstream= (X+Y) km/hr

And, the speed of the boat or swimmer against the stream is known as speed upstream. It is given by;

Speed upstream= (X-Y) km/hr

2) Speed of man or boat in still water is given by;

( speed downstream + speed upstream)

3) Speed of the stream is given by;

=  ( speed downstream – speed upstream)

4) A man can row at a speed of X km/hr in still water. If the speed of the stream is Y km/hr and the man rows the same distance up and down the stream, his average speed for the entire journey is given by;

=

km/hr

5) A man can row a boat in still water at X km/hr. If the stream is flowing at Y km/hr it takes him t hours more to row upstream than to row downstream to cover the same distance. The distance is given by;

Distance =

6) A man can swim in still water at X km/hr. If the stream is flowing at Y km/hr it takes him t hours to reach a place and return back to the starting point. The distance between the place and the starting point is given by;

Distance =

7) A boat or swimmer covers a certain distance downstream in t1 hours and returns the same distance upstream in t2 hours. If the speed of the stream is Y km/hr, the speed of boat or man in still water is given by;

= Y  km/hr

8) A boat or swimmer takes K times as long to move upstream as to move downstream to cover a certain distance. If the speed of the stream is Y km/hr, the speed of the boat or man in still water is given by;

= Y  km/hr

Boat & Stream Solved Sample Questions

Q 1. A person can swim in water with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, what will be the time taken by the person to go 68 km downstream?

  1. 5 hours
  2. 3 hours
  3. 4 hours
  4. 5 hours
  5. 5 hours

Answer: (3) 4 hours

Solution:

Downstream Speed = (13+4) km/hr = 17 km/hr

To travel 68 km downstream.

Time taken = 68/17 = 4 hours

Q 2. In one hour, a boat goes 13 km/hr in the direction of the stream and 7 km/hr against the direction of the stream. What will be the speed of the boat in still water?

  1. 8 km/hr
  2. 10 km/hr
  3. 14 km/hr
  4. 6 km/hr
  5. Cannot Be Determined

Answer: (2) 10 km/hr

Solution:

According to the formula,

Speed of a boat in still water = ½ (DownstreamSpeed + UpstreamSpeed)

Speed of boat in still water = ½ (13+7) = ½ × 20 = 10 km/hr

Q 3. A woman can row upstream at 16 km/hr and downstream at 26 km/hr. What is the speed of the stream?

  1. 5 km/hr
  2. 2 km/hr
  3. 5 km/hr
  4. 21 km/hr
  5. 12 km/hr

Answer: (1) 5km/hr

Solution:

According to the formula,

Speed of the stream = ½ (Downstream Speed – Upstream Speed)

Speed of the stream = ½ (26-16) = ½ × 10 = 5 km/hr

Q 4. A speedboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. What is the speed of the stream in km/hr?

  1. 5 km/hr
  2. 5 km/hr
  3. 4 km/hr
  4. 5 km/hr
  5. 25 km/hr

Answer: (4) 5 km/hr

Solution:

Let the speed of the stream be x km/hr

Upstream Speed = 15 + x

Downstream Speed = 15 – x

So, {30 / (15+x)} + {30 / (15-x)} = 4 ½ (4 hours 30 minutes)

⇒ {900 / (225-x2)} = 9/2

⇒ 9×2 = 225

⇒x2 = 25

⇒x = 5

Q 5. A boat is moving 2 km against the current of the stream in 1 hour and moves 1 km in the direction of the current in 10 minutes. How long will it take the boat to go 5 km in stationary water?

  1. 1 hr 20 minutes
  2. 1 hr 30 minutes
  3. 1 hr 15 minutes
  4. 30 minutes
  5. 45 minutes

Answer: (3) 1 hr 15 minutes

Solution: 

Downstream = (1/10 × 60) = 6 km/hr

Upstream = 2 km/hr

Speed in still water = ½ (6+2) = 4 km/hr

So, the time is taken by the boat to go 5km in stationary water = 5/4 hrs = 1 ¼ hrs = 1 hr 15 minutes

Download Boat & Stream Sample Questions PDF

Boat & Stream Important Questions

Ques1. A man’s speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man’s speed against the current is:

  1. 9 km/hr
  2. 12.5 km/hr
  3. 8.5 km/hr
  4. 10 km/hr.

Answer: Option 4

Explanation:

Man’s speed with the current = 15 km/hr

=> speed of the man + speed of the current = 15 km/hr

speed of the current is 2.5 km/hr

Hence, speed of the man = 15 – 2.5 = 12.5 km/hr

man’s speed against the current = speed of the man – speed of the current

= 12.5 – 2.5 = 10 km/hr

Ques2. A man takes 20 minutes to row 12 km upstream which is a third more than the time he takes on his way downstream. What is his speed in still water?

  1. 41 km/hr
  2. 36 km/hr
  3. 42 km/hr
  4. 45 km/hr

Answer: Option 3

Explanation:

Let the speed in still water = x km/hr.

Takes 20 minutes to row 12 km upstream ⇒ speed of u/s = 36 km/hr.

Also, time taken for u/s is 1/3 more than for d/s.

∴ distance covered in d / s will be 1/3 more.

Hence distance covered by man for d / s in 20 minutes = 12 × (12/3) = 16km.

So speed of d / s = 48 km/hr.

∴ x + y = 48 and x – y = 36 ⇒ x = 42 km/hr.

Ques3. How long will it take to row 20 km upstream if one can row 10 km in 10 minutes in still water and the same distance in 8 minutes with the stream?

  1. 12 min
  2. 13.33 min
  3. 24 min
  4. 26.67 min

Answer: Option 4

Explanation:

Let x be the speed of man in still water and y be the speed of stream.

∴ Speed of man (x) = 60 km/hr and speed of downstream = 75 km/hr.

∴ Speed of stream = 15 km/hr.

Hence upstream speed = 60 – 15 = 45 km/hr.

So time taken to cover 20 km = 20/45*60 = 26.67min.

Ques4. A boat makes a return journey from point A to point B and back in 5 hours 36 minutes. One way it travels with the stream and on the return it travels against the stream. If the speed of the stream increases by 2 km/hr, the return journey takes 9 hours 20 minutes. What is the speed of the boat in still water? (The distance between A and B is 16 km.)

  1. 5 km/hr
  2. 3 km/hr
  3. 7 km/hr
  4. 9 km/hr

Answer: Option 3

Explanation:

Let x be speed of u / s and y be the speed of d / s.

∴ (16/x) + (16/y) = (28/5) and 16/(y+2) + 16/(x-2) = 28/3

Solving these 2 equations, we get x = 4km/hr and y = 10km/hr

∴ speed of boat in still water = (4+10) / 2 = 7km/hr.

 Ques5. A boat travels from point A to B, a distance of 12 km. From A it travels 4 km downstream in 15 minutes and the remaining 8 km upstream to reach B. If the downstream speed is twice as high as the upstream speed, what is the average speed of the boat for the journey from A to B?

  1. 10(2/3)km/hr
  2. 9.6 km/hr
  3. 11.16 km/hr
  4. 10.44 km/hr

Answer: Option 2

Explanation:

4 km downstream is covered in 15 min.

∴ speed of downstream = 16 km/hr.

So speed of upstream = 8km/hr.

Total time taken for downstream journey = 15 min (given).

Now total time taken for upstream journey = 8/8 = 1 hr = 60 min.

Hence total time taken from A to B = 15 + 60 = 75 min.

As average speed = Total distance /total time, so average speed from A to B = (12/75)*60 = 48/5 = 9.6kmph.

Ques6. A man rows ‘k’ km upstream and back again downstream to the same point in H hours. The speed of rowing in still water is s km/hr and the rate of stream is r km/hr. Then

  1. (s2-r2) =2sk /H
  2. (r + s) = kH / (r -s)
  3. rs = kH
  4. None of the above

Answer: Option 1

Explanation:

Time taken to cover total distance = H hrs.

Speed of upstream = s – r.

Speed of downstream = s + r.

∴ k / (s + r) + k / (s – r) = H ⇒(s2-r2) =2sk /H

 Ques7. A man rows 24 km upstream in 6 hours and a distance of 35 km downstream in 7 hours. Then the speed of the man in still water is

  1. 4.5 km/hr
  2. 4 km/hr
  3. 5 km/hr
  4. 5.5 km/hr

Answer : Option 1

Explanation:

Speed of upstream = 24 / 6 = 4 km / hr.

Speed of downstream = 35 / 7 = 5km / hr.

∴ Speed of man in still water = (4 + 5) / 2 = 4.5 km / hr.

 Ques8. A boat goes 12 km upstream in 48 minutes. The speed of stream is 2 km/hr. The speed of boat in still water is

  1. 15 km/hr
  2. 16 km/hr
  3. 17 km/hr
  4. 18 km/hr

Answer: Option 3

Explanation:

12 km upstream in 48 min.

⇒ it will cover 15 km in 1 hr.

Speed of stream = 2 km / hr.

∴ Speed of boat in still water = 15 + 2 = 17 km / hr.

Ques9. A motorboat can travel at 5 km/hr in still water. It travelled 90 km downstream in a river and then returned, taking altogether 100 hours. Find the rate of flow of the river.

  1. 3 km/hr
  2. 3.5 km/hr
  3. 2 km/hr
  4. 4 km/hr

Answer: Option 4

Explanation:

Speed of boat in still water = x = 5 km/hr.

Let rate of flow of river = y km/hr.

∴ Speed of u/s = 5- y and speed of d / s = 5 + y

∴ 90/(5+y) + 90/(5-y) = 100 ⇒ y = 4 km/hr.

Ques10. A boatman can row 2 km against the stream in 20 minutes and return in 10 minutes. Find the rate of flow of the current.

  1. 2 km/h
  2. 1 km/h
  3. 3 km/h
  4. 5 km/h

Answer: Option 3

Explanation:

Let x be the speed of man in still water and y be the speed of current.

Speed of d / s = (2 / 10) × 60 = 12 km / hr.

Speed of u / s = (2 / 20) × 60 = 6 km / hr.

∴ rate of current = (12 – 6) / 2 = 3 km/hr.

Download PDF: Boat & Stream Important Questions

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