# Boat & Stream – Concept, Formula, Tips & Questions

# Boat & Stream - Concept, Formula, Tips & Questions

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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

## Boat and Stream – Concept

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.

## Upstream and Downstream – Formula

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 = {(u**^{2}**-v**^{2}**) × 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 = {(u**^{2}**-v**^{2}**) × 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:

### Types of Questions

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:

### Tips and Tricks to Solve Boat and Stream Questions

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:

**1)A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.**

A. 2 hours

B. 3 hours

C. 4 hours

D. 5 hours

Speed downstream = (13 + 4) km/hr = 17 km/hr.

Time taken to travel 68 km downstream = | 68 | hrs = 4 hrs. | |

17 |

**2)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:**

A. 8.5 km/hr

B. 9 km/hr

C. 10 km/hr

D. 12.5 km/hr

Man’s rate in still water = (15 – 2.5) km/hr = 12.5 km/hr.

Man’s rate against the current = (12.5 – 2.5) km/hr = 10 km/hr.

**3)A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 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. 2 : 1

B. 3 : 2

C.8 : 3

D. Cannot be determined

Let the man’s rate upstream be *x* kmph and that downstream be *y* kmph.

Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.

x x 8 | 4 | = (y x 4) | |||

5 |

44 | x =4y | |

5 |

y = | 11 | x. |

5 |

Required ratio = | y + x | : | y – x | ||||

2 | 2 |

= | 16x | x | 1 | : | 6x | x | 1 | ||||

5 | 2 | 5 | 2 |

= | 8 | : | 3 |

5 | 5 |

= 8 : 3.

**4)A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:**

A. 4

B. 5

C. 6

D. 10

Let the speed of the stream be *x* km/hr. Then,

Speed downstream = (15 + *x*) km/hr,

Speed upstream = (15 – *x*) km/hr.

30 | + | 30 | = 4 | 1 | |

(15 + x) | (15 – x) | 2 |

900 | = | 9 | |

225 – x^{2} | 2 |

9*x*^{2} = 225

*x*^{2} = 25

*x* = 5 km/hr.

**5) In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:**

A. 3 km/hr

B. 5 km/hr

C. 8 km/hr

D. 9 km/hr

Speed in still water = | 1 | (11 + 5) kmph = 8 kmph. |

**6) A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?**

A. 4 km/hr

B. 6 km/hr

C. 8 km/hr

D. 9 km/hr

Rate downstream = | 16 | kmph = 8 kmph. | |

2 |

Rate upstream = | 16 | kmph = 4 kmph. | |

4 |

Speed in still water = | 1 | (8 + 4) kmph = 6 kmph. |

**7) The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is:**

A. 3 km/hr

B. 5 km/hr

C. 2.4 km

D. 3.6 km

Speed downstream = (15 + 3) kmph = 18 kmph.

Distance travelled = | 18 x | 12 | km = 3.6 km. | |

60 |

**8) A boat takes 90 minutes less to travel 36 miles downstream than to travel the same distance upstream. If the speed of the boat in still water is 10 mph, the speed of the stream is:**

A. 2 mph

B. 2.5 mph

C. 3 mph

D. 4 mph

Let the speed of the stream *x* mph. Then,

Speed downstream = (10 + *x*) mph,

Speed upstream = (10 – *x*) mph.

36 | – | 36 | = | 90 | |

(10 – x) | (10 + x) | 60 |

72*x* x 60 = 90 (100 – *x*^{2})

*x*^{2} + 48*x* – 100 = 0

(*x*+ 50)(*x* – 2) = 0

*x* = 2 mph.

**9) A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?**

A. 2.4 km

B. 5 km/hr

C. 8 km/hr

D. 9 km/hr

Speed downstream = (5 + 1) kmph = 6 kmph.

Speed upstream = (5 – 1) kmph = 4 kmph.

Let the required distance be *x* km.

Then, | x | + | x | = 1 |

6 | 4 |

2*x* + 3*x* = 12

5*x* = 12

*x* = 2.4 km.

**10) A boat covers a certain distance downstream in 1 hour, while it comes back in 1 1/2 hours. If the speed of the stream is 3 kmph, what is the speed of the boat in still water?**

A. 12 kmph

B. 13 kmph

C. 14 kmph

D. 15 kmph

Let the speed of the boat in still water be *x* kmph. Then,

Speed downstream = (*x* + 3) kmph,

Speed upstream = (*x* – 3) kmph.

(x + 3) x 1 = (x – 3) x | 3 |

2 |

2*x* + 6 = 3*x* – 9

*x* = 15 kmph.

**11) A boatman goes 2 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 5 km in stationary water?**

A. 40 minutes

B. 1 hour

C. 1 hr 15 min

D. 1 hr 30 min

Rate downstream = | 1 | x 60 | km/hr = 6 km/hr. | |

10 |

Rate upstream = 2 km/hr.

Speed in still water = | 1 | (6 + 2) km/hr = 4 km/hr. |

2 |

Required time = | 5 | hrs = 1 | 1 | hrs = 1 hr 15 min. |

**12) A man can row three-quarters of a kilometre against the stream in 11 1/4 minutes and down the stream in 7 1/2 minutes. The speed (in km/hr) of the man in still water is:**

A. 2

B. 3

C. 4

D. 5

We can write three-quarters of a kilometre as 750 metres,

and 11 minutes as 675 seconds.

Rate upstream = | 750 | m/sec | = | 10 | m/sec. | |

675 | 9 |

Rate downstream = | 750 | m/sec | = | 5 | m/sec. | |

450 | 3 |

Rate in still water = | 1 | 10 | + | 5 | m/sec | |

2 | 9 | 3 |

= | 25 | m/sec |

18 |

= | 25 | x | 18 | km/hr | |

18 | 5 |

= 5 km/hr.

**13) Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:**

A. 16 hours

B. 18 hours

C. 20 hours

D. 24 hours

Speed upstream = 7.5 kmph.

Speed downstream = 10.5 kmph.

Total time taken = | 105 | + | 105 | hours = 24 hours |

**14) A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:**

A. 2 : 1

B. 3 : 1

C. 3 : 2

D. 4 : 3

Let man’s rate upstream be *x* kmph.

Then, his rate downstream = 2*x* kmph.

(Speed in still water) : (Speed of stream) = | 2x + x | : | 2x – x | ||||

2 | 2 |

= | 3x | : | x |

2 | 2 |

= 3 : 1.

**15)A man rows to a place 48 km distant and come back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 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

Suppose he move 4 km downstream in *x* hours. Then,

Speed downstream = | 4 | km/hr. | ||

x |

Speed upstream = | 3 | km/hr. | ||

x |

48 | + | 48 | = 14 or x = | 1 | . | |

(4/x) | (3/x) | 2 |

So, Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.

Rate of the stream = | 1 | (8 – 6) km/hr = 1 km/hr. |

2 |