Boats and Streams for CAT

Questions from boats and streams are one of the most frequent questions in the CAT quantitative aptitude section. The questions related to boats and streams are easily solvable and scoring. It is always suggested to be well prepared with the concepts and formulas of boats and streams to be able to solve any question in the exam. Here is a detailed guide to boats and stream questions for the CAT with solved examples.

Commonly Asked Question in Boats and Streams:

  • Time Related Questions

The speed of the stream and the speed of the boat in still water will be given and the question will be to find the time taken by a boat to go downstream or upstream or both.

 

  • Speed Related Questions

The speed of a boat in upstream and downstream will be given and the candidates will be asked to find the speed of the boat in still water or the speed of the stream.

 

  • Average Speed Questions

The average speed of boat can be asked. Here, the speed of the boat in upstream and downstream will be provided in the question.

 

  • Distance Related Questions

In this, the distance travelled will be asked. The time taken by the boat to reach a point in upstream and downstream will be given.

 

Important Terms and Formulas in Boats and Streams:

In boats and streams, it is important to get acquainted with certain terms to be able to understand the conditions and solve the questions accordingly. Some of the most important terms and certain conditions are explained below.

 

First, consider the following notations:

u= Speed of the boat in still water

v= Speed of the stream

 

  • Upstream:

The term upstream refers to a condition when the boat moves opposite to the direction of the stream. At this time, the speed of the boat is reduced as it moves against the stream.

\(Upstream\, Speed= \left ( u-v \right )Km/hr\)

 

  • Downstream:

When a boat moves downstream, it simply means that the boat is moving in the direction of the stream. In this case, the speed of the boat increases as it moves along the stream.

\(Downstream\, Speed= \left ( u+v \right )Km/hr\)

 

  • Still Water

In still water, the water is stationary i.e. speed of the stream is zero. The speed of the boat in still water can be calculated as follows.

\(Speed\, in\, Still\, Water=\frac{1}{2}\left ( Downstream\, Speed + Upstream\, Speed \right )\)

 

  • Stream:

A stream simply refers to the flowing of either water or river at a certain speed. The formula to calculate the speed of the stream is given below.

\(Speed\, of\, Stream=\frac{1}{2}\left ( Downstream\, Speed – Upstream\, Speed \right )\)

 

  • Average Speed

The average speed of a boat can be calculated using its speed in still water and the speed of the stream. The formula is:

\(Average\, Speed=\frac{\left ( Upstream\, Speed \right )\times\left ( Downstream\, Speed \right ) }{Boat’s\, Speed\, in\, Still\, Water}\)= \(\frac{\left ( u-v \right )\times \left ( u+v \right )}{u}km/hr\)

 

  • Distance

Case 1: If a boat takes “t” hours to reach a point in still water and comes back to the same point then, the distance between that point and the starting point can be calculated as:

\(Distance=\frac{\left ( u^{2}-v^{2} \right )\times t}{2u}Km\)

 

Case 2: If a boat takes “t” hours more to go to a point in upstream than in downstream for the same distance, the distance will be:

\(Distance=\frac{\left ( u^{2}-v^{2} \right )\times t}{2v}Km\)

 

  • Speed When Time is Given

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:

\(Speed=v\left ( \frac{t2+t1}{t2-t1} \right )Km/hr\)

 

Additional Case:

If a boat takes “n” times as long to go upstream as to go downstream the stream then,

\(u=v\left ( \frac{n+1}{n-1} \right )\)

 

Example Questions on Boats and Streams

Example 1:

What would be the time taken by a boat to go 80 km downstream if the speed of the stream is 5 km/hr and the boat’s speed in still water is 15km/hr?

Solution:

Downstream speed of the boat= (15 + 5)= 20 km/hr.

Time taken by the boat to go 80 km downstream= (80/20) hours= 4 hrs.

 

Example 2:

In an hour, a boat travels 20 km/hr along the stream and 10 km/hr against the stream. Calculate the speed of the boat in still water.

Solution:

From the formula, the speed in still water= ½ (20+10)= 15 km/hr.

 

Example 3:

What would be the speed of a boat in still water if it covers a distance of 40 km in 4 hours in upstream and covers 40 km in 2 hours while going downstream?

Solution:

From the data, upstream speed= (40/4)= 10 km/hr.

And, downstream speed= (40/2)= 20 km/hr.

So, the speed of the boat= ½ (10 + 20)= 15 km/hr.

 

It is always suggested to practice a wide range of questions from this topic to be able to confidently tackle different variations of questions in the CAT exam. For more such study materials for CAT topics, keep visiting BYJU’S.