Boats and Streams Related Questions

Boats and streams-related questions are very commonly used in various competitive exams. Being tricky, these questions are considered important for exams on a national level or government-conducted exams. These questions are usually found in the Quantitative Aptitude Section of various exams conducted by the government. These questions are based on major concepts of boats and streams. All the important concepts like upstream, downstream, still water, etc. are utilised in formulating these questions. The tricks and tips to solve the boats and streams-related problems are present in various formulas for the same. 

Concepts About Boats and Streams

There is a wide range of concepts about boats and streams problems. Some of the major concepts related to boats and streams are mentioned below:

1. Stream – A stream is used to refer to running river water.
2. Upstream – When the boat rows or moves in the opposite direction of the flow of the stream, it is said to be moving upstream. The boat’s net speed, in this case, is upstream speed.
3. Downstream – When the boat rows or moves along the direction of the flow of the stream, it is said to be moving downstream. The boat’s net speed, in this case, is downstream speed.
4. Still Water – Still water is the assumption of water being still or stationary. This happens when the speed of the water is zero.

Formulas for Upstream and Downstream Problems

Below are the important formulas for the various boats and streams concepts.

To calculate,

• Upstream = (u−v) km/hr
• Boat’s speed in still water = ½ (Downstream Speed + Upstream Speed)
• Downstream = (u+v)Km/hr
• Boat’s average speed = {(Upstream Speed x Upstream Speed)/Boat’s Speed in Still Water}
• Stream’s Speed = ½ (Downstream Speed – Upstream Speed) 
• Boat’s Speed (Still Water) = ½ (Downstream Speed + Upstream Speed)
• Distance (X) between two points, when the time taken to come back to the starting point is ‘t’ = {(u2-v2) x t } / 2u.
• Distance (X) between two points situated upstream and downstream when the time taken to cover going back and forth is ‘t’ = {(u2-v2) × t} / 2v.

Various Classifications for Boats and Streams Questions

The boats and streams questions can be broadly classified into four types based on various formulas applied. These types are:

1. Questions based on time: As the name itself is suggestive, these questions include the calculation of time. It will most probably be a calculation of the time a boat takes to travel downstream or upstream. 
2. Questions based on average speed: One of the easiest types of boats and streams questions is average speed calculation. With the given data on upstream and downstream speeds, the average speed is calculated using the formula.
3. Questions based on distance: These are the questions where the calculation of distance the boat covers whether downstream or upstream is calculated. In these questions, the time, as well as the speed of the stream, are mentioned.
4. Questions based on speed: These are the questions for calculating the speed of a boat or the stream.

Solving Boats and Streams Questions: Tricks and Tips

Some important tricks and tips for solving boats and streams questions are:

• The first step to solving the boats and streams problems is to thoroughly read the question with a calm mind. This helps understand the various terms behind the boats and stream concepts being applied.
• If upstream and downstream are not mentioned, do not be confused. You should remember that motion opposite to the flow of the stream is upstream and motion along the flow of the stream is downstream.
• Do not forget to memorise the formulas related to boat and stream problems. Regularly going through the formulas will help memorise them. Knowing the exact formula required for a particular question helps solve the question easily.
• The last, but not the least, a tip is constant practice. You will be able to solve the questions easily if you have been in practice.

Boats and streams Questions: Solved Examples

Here are a few solved examples of boat and streams problems for reference.

Ques 1. Sudesh in still water has recorded a row speed of 14 km/h. He takes thrice the time of rowing down the river to row up the river. What is the rate of this stream? 

Solution:

Sudesh’s speed in still water = 14 km/h

n = 3, 

Stream’s speed (x) =?

The formula for speed in still water = x(n+1)/(n-1)

14 = x (3+1)/(3-1)

2x = 14

a = 14/2

= 7 km/h

Ques 2. The rowing speed of a man is 14 km/hr (in still water). If the river runs at a rate of 3 km/hr, it takes 2 hours to row and come back from a place. At what distance is this place?

Solution:

Man’s speed in still water = a =14 km/h

River’s Speed = b = 3 km/hr

Time is taken T = 2 hr

The distance between the places(x) = T(a²-b²)/2a

= 1 x [(14)²-(3)²1/2×14 = 187/28

x =6.67 km

Ques 3. The rowing speed of Sid in still water is 5 km per hour for reaching a place. What will be the average speed during the whole journey if the rate of flow of the river is 2 km per hour?

Solution:

Given,

X = 5 km/hr 

Y = 2 km/hr 

The formula for average speed is,

(X+Y)(X-Y)/X

= [{(5+2) (5-2)}/ 5] 

= {(7 x 3)/5}

= 21/5

Average dpeed = 4.2 km/hr

Conclusion

Boats and streams related problems are usually based on the major concepts of boats and streams. The involvement of these concepts makes the boats and streams problems more tricky as well as easy to predict. Understanding the concepts like downstream, upstream, still, water, etc. are very important to solve these problems. Boats and stream problems mostly focus on the speed of the boat, the speed of the stream, the time taken to cover a distance, and the distance covered in a given time. With the correct tips and tricks, these can be easily solved.