Boat & Stream - Concept, Formula, Tips & Questions

The boat and stream concept is one of the most common topics based on which questions are asked in the various Government exams conducted in the country. 

The boat and stream questions are asked in the quantitative aptitude section of the Government exams and the weightage of questions mostly varies between 1-3 marks. 

In this article, we shall discuss the boat and stream topic concept, tips to solve the questions, important formulas and some sample questions to have a better understanding of the topic.

For any competitive exam candidate who is willing to make his/her way into a job career in the Government sector, having knowledge of all important topics and syllabus for the exams is extremely important. 

Given below are a few other Quantitative Aptitude related topics for the reference of candidates:

Boat & Stream – Sample Questions PDF:-Download PDF Here

There are a variety of subconcepts that are related to answering questions based on boat and streams concept. Given below are the four terms which are important for a candidate to know to understand the concept of streams.

• Stream – The moving water in a river is called a stream. 
• 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
• 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
• Still Water – Under this circumstance the water is considered to be stationary and the speed of the water is zero

The questions from this topic may seem to be confusing until a candidate is aware of the above-mentioned terms and how they may be used for answering the questions. 

This topic basically deals with calculating the speed of anything in the water when it flows along with the flow of water or in the opposite direction.

Given below are a few important formulas with the help of which you can solve the questions based on boat and streams. 

Candidates must learn these formulas by heart to ensure they are able to answer the simple formula based questions correctly and do not end up losing marks for direct questions. 

• Upstream = (u−v) km/hr, where “u” is the speed of the boat in still water and “v” is the speed of the stream
• Downstream = (u+v)Km/hr, where “u” is the speed of the boat in still water and “v” is the speed of the stream
• Speed of Boat in Still Water = ½ (Downstream Speed + Upstream Speed)
• Speed of Stream = ½ (Downstream Speed – Upstream Speed)
• Average Speed of Boat = {(Upstream Speed × Downstream Speed) / Boat’s Speed in Stii Water}
• If it takes “t” hours for a boat to reach a point in still water and comes back to the same point then, the distance between the two points can be calculated by Distance = {(u²-v²) × t} / 2u, where “u” is the speed of the boat in still water and “v” is the speed of the stream
• If it takes “t” hours more to go to a point upstream than downstream for the same distance, the formula for distance will be: Distance = {(u²-v²) × t} / 2v, where “u” is the speed of the boat in still water and “v” is the speed of the stream
• If a boat travels a distance downstream in “t1” hours and returns the same distance upstream in “t2” hours, then the speed of the man in still water will be: Speed of Man in Still Water = [v × {(t2+t1) / (t2-t1)}] km/hr, where“v” is the speed of the stream

The above-given formulas will help you answer the direct questions easily if you memorise the formulas well. 

Candidates can refer to the below-mentioned links to prepare themselves for the different topics under the Government exam syllabus:

The questions from this topic may usually be asked in four different formats. These include:

• Time Based Questions – The time taken by a boat to travel upstream or downstream may be asked with the speed of a boat in still water and speed of the stream given in the question
• Speed Based Questions – Questions to find the speed of the stream or the speed of the boat in still water may be asked 
• Questions on Average Speed – With the speed of the boat upstream and downstream given in the question, the average speed of the boat may be asked
• Questions Based on Distance – The distance travelled by boat upstream or downstream may be asked 

These are the four basic types of questions that are asked related to the boat and streams topic in the Government exams.

Given below is the syllabus for various Government exams where candidates can not just find the quantitative aptitude syllabus but also the topics for other subjects:

For candidates who are new to this concept, the questions may prove to be confusing and complex. But once the candidate solves questions based on this topic, he/she is more likely to get a hang of the questions asked and also solve them quickly and more efficiently.

Given below are a few tricks which may help you solve the boat and stream questions from the quantitative aptitude section faster and without making any errors:

• The first and most important tip is that a candidate must memorise the important formulas to answer the questions correctly. Memorising the formulas will help candidates answer straight forward questions without making any errors
• Do not confuse yourselves between the concept of upstream and downstream as the question may not specifically mention the two terms and instead mention “ in the direction of flow” or “against the direction of flow”
• Reading the questions carefully will help candidates avoid making silly mistakes, so do not be in a rush while reading the instructions mentioned in the article
• Ensure that you do not panic reading the length of the question or the terms used in the questions as boat and stream questions asked in the Government exams are mostly direct and not too complex. It is just the formation of the question that makes it sound complicated

Furthermore, it must be noted that the more a person applies the formulas to the questions, the more likely is it that he/she may answer questions with accuracy. Only practising hard can make a candidate ace the exam. 

Candidates can check the video given below and get a simpler explanation of the boat and stream-based questions asked in the competitive exams from the experts themselves:

Given below are a few sample boat and stream questions with solutions that may help you understand the concept better.

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. 2.5 hours
2. 3 hours
3. 4 hours
4. 3.5 hours
5. 4.5 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. 4.5 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. 2.5 km/hr
2. 3.5 km/hr
3. 4 km/hr
4. 5 km/hr
5. 3.25 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

⇒ 9x² = 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

Boat & Stream – Sample Questions PDF:-Download PDF Here

Candidates must go through the questions given above and start their preparation for the upcoming competitive exams. 

For more information regarding the upcoming exams, syllabus, study material and any other relevant data, candidates can turn to BYJU’S for assistance.