Boats & Streams Aptitude Questions 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 easy to solve and are high 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 upstream and downstream will be given and 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 the boat can be asked. Here, the speed of the boat upstream and downstream will be provided in the question.
  • Distance Related Questions: In this, the distance traveled will be asked. The time taken by the boat to reach a point 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.

\(\begin{array}{l}Upstream\, Speed= \left ( u-v \right )Km/hr\end{array} \)

  • 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.

\(\begin{array}{l}Downstream\, Speed= \left ( u+v \right )Km/hr\end{array} \)

  • 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.

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

  • 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.

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

  • 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:

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

  • 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:

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

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:

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

  • 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:

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

Additional Case:

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

\(\begin{array}{l}u=v\left ( \frac{n+1}{n-1} \right )\end{array} \)

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.

Let’s Look at Some of The CAT Boats & Streams Aptitude Questions From Previous Year Papers:

Take ⅕ or 2 minutes each and then, check the solutions given in the end

Q1. 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.

Ans. 1. 2 hours

2. 3 hours

3. 4 hours

4. 5 hours

Q2. 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?

Q3. 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:

Ans. 1. 8.5 km/hr

2. 9 km/hr

3. 10 km/hr

4. 12.5 km/hr

Q4. 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.

Q5. A boat takes 28 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 6km/hr and the speed of the boat in still water is 9 km/hr, what is the distance between A and B?

Ans. 1. 115 kms

2. 120 kms

3. 140 kms

4. 165 kms

Q6. 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?

Q7. 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:

Ans. 1. 3 km/hr

2. 5 km/hr

3. 8 km/hr

4. 9 km/hr

Q8. A boat running upstream takes 9 hours 48 minutes to cover a certain distance, while it takes 7 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?

Ans. 1. 5:2

2. 7:4

3. 6:1

4. 8:3

Q9. A boat can travel 20 km downstream in 24 min. The ratio of the speed of the boat in still water to the speed of the stream is 4 : 1. How much time will the boat take to cover 15 km upstream?

Ans 1. 20 mins

2. 22 mins

3. 25 mins

4. 30 mins

Q.10. A boat whose speed in 20 km/hr in still water goes 40 km downstream and comes back in a total of 5 hours. The approx. speed of the stream (in km/hr) is:

Ans 1. 6 km/hr

2. 9 km/hr

3. 12 km/hr

4. 16 km/hr

Answer Keys:

Q1 – Option 3

Solution –

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

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

Q2.

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.

Q3. – Option 3

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.

Q4.

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

Q5. – Option 2

Downstream speed = 9+6 = 15

Upstream speed = 9-6 = 3

Now total time is 28 hours

If distance between A and B is d, then distance BC = d/2

Now distance/speed = time, so d/15 + (d/2)/3= 28

Solved = 120 kms

Q6.

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.

Q7. – Option 3

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

Q8. Option 3

Distance covered upstream in 9 hrs 48 min = Distance covered downstream in 7 hrs

(X-Y) 49/5 = (X+Y) 7

X/Y = 1/6

Q9. Option 4-

Down speed =20/24*60=50km/hr

4:1 =4x:x

Downstream speed = 4x+x=5x

Upstream speed = 4x-x=3x

5x= 50; x=10

so up speed 3*10=30

Time = 15/30*60= 30 mins

Q10. Option 2

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

Speed downstream = (20 + x) km/hr, Speed upstream = (20 – x) km/hr.


40/20+x + 40/20-x = 5


X = 9 km/hr appx.