# Boats and Streams Questions

This post is a collection of Boats and Stream quantitative aptitude questions that have been previously asked in competition exams. In order to solve these questions you should have clear understanding of the concepts of Time, Speed and Distance, I would strongly suggest to read that chapter before solving the below questions.

All the questions are step by step solved so that the student of weak Math background can easily grasp the solution. I hope my selection of questions will help clear your dream exam

## Boat and Stream Aptitude Questions

(01) 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?

Given:
Distance = 16 km, in time = 2 hours (downstream)

To find =
Speed, when time = 4 hours (upstream)

Speed at downstream = distance/ time = 16/2 kmph = 8 kmph
Speed at upstream = distance/ time = 16/4 kmph = 4 kmph

Therefore, speed of boat in still water = ½ (speed of downstream + speed of upstream) kmph

=½ x (8 + 4) kmph

=½ x (12) kmph

=6 kmph

Therefore speed of boat in still water is 6 kmph.

(02) 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?

Given:
Time for upstream = 8 hours 48 minutes
Time for downstream = 4 hours

To Find:
ratio between speed of boat and speed of water current

Let us suppose the upstream speed rate be x kmph
while that of downstream speed rate be y kmph

As we know that,
the distance covered upstream in 8 hours 48 minutes = distance covered downstream in 4 hours

Therefore, (speed x time) upstream = (speed x time) downstream

(x. 8 4/5) = (y x 4)   ( since 48 minute is 4/5th part of 60 min or 1 hour)

44/5. x = 4y

y = 11/5.x

Therefore, ratio of speed of boat and speed of water =
[(Speed downstream + speed upstream)/2] : [(speed downstream – speed upstream/2)]

= [(x + y/2)] : [(y -x/2)]

= [(x + 11/5.x)/2] : [(11/5.x – x)/2]  (putting the value          of y here)

= [(5x + 11x)/2] : [(11x – 5x)/2]

= 16x/2 : 6x/2

= 8x : 3x

= 8:3

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

Given:
Speed of boat in still water = 13kmph
Speed of stream  = 4 kmph

To Find:
Distance = 68 km in time = ?

Speed downstream = speed of boat in still water + speed of stream

= (13 + 4) kmph

= 17 kmph

Time taken to travel 68 km downstream = distance/ speed = 68/17 hours = 4 hours

Ans. Time taken by boat to downstream is 4 hours.

(04) 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?

Given:
Speed of man to row in still water = 5 kmph
Velocity of current = 1 kmph
Time to row a place and come back = 1 hour

To find: distance

Now, speed downstream  = speed of boat in still water + Speed of stream

= (5 + 1) kmph = 6 kmph

Speed upstream  = Speed of boat in still water – speed of stream

= (5 – 1) kmph

= 4 kmph

Let the distance to be x km,
Then total time = downstream time + upstream time

1 = x/6 + x/4    (since, time = distance/speed) (time in rowing and come and             back= 1 hour)

24 = 4x + 6x

24 = 10 x

x = 2.4 km

Ans. The place is 2.4 km far.

(05) 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:

Let us suppose the rate of man to row a distance in favor of  the stream to be 2x kmph,
Then according to question, the rate of man to row a distance against the stream = x kmph

To find:
Ratio of speed of boat in still water to the stream

Therefore, (speed in still water) : (speed in stream) = [½  (downstream speed + upstream speed)] :

[1/2 (downstream speed – upstream speed)]

= [1/2 . (2x + x)] : [1/2 . (2x – x)]

= [1/2 x 3x] : [1/2 x x]

=3x/2 : x/2

= 3 : 1

Ans. The ratio of given speed is 3 :1

Q6. A man rows a boat 18 kilometers in 4 hours down-stream and returns upstream in 12 hours. The speed of the stream (in km per hour) is:

(a) 1                       (b) 1.5

(c) 2                       (d) 1.75

Solution
Rate of Down stream = 18/4 = 9/2 km/hr

Rate of Upstream = 18/12 = 3/2 km/hr

Speed of Stream = (Rate of downstream – Rate of upstream) / 2

Speed of Stream = (9/2 – 3/2) / 2

Speed of Stream = 1.5 km/hr

Option (b) is the right answer

Q7. A boat goes 20 km downstream in one hour and the same distance upstream in two hours. The speed of the boat in still water is

(a) 15 km/hr       (b) 10 km/hr

(c) 5 km/hr          (d) 7.5 km/hr

Solution
Let the speed of boat be p km/hr
Rate of stream = q km/hr

Rate of downstream = (p + q) km/hr
Rate of upstream = (p – q) km/hr

option (a) is the right answer

Q8. A man rows 750 m in 675 seconds against the stream and return in minutes. Find its rowing speed in still water.

(a) 3 kmph          (b) 4 kmph

(c) 5 kmph           (d) 6 kmph

Solution
Rate of down stream = 750/675 = 10/9 m/sec
Rate of up stream = 750/450 = 5/3 m/sec

Rate in still water = (Rate of down stream + Rate of upstream )/2

Rate in still water = ( 10/9 + 5/3 )/ 2 = 25/18 m/sec

Converting m/sec into Km/hr by multiplying 18/5
=> 25/18 * 18/5
=> 5 Km/hr

Option (c) is the right answer

Q9. A boat goes 6 km an hour in still water, it takes thrice as much time in going the same distance against the current comparison to direction of current. The speed of the current (in km/hour) is

(a) 4                       (b) 5

(c) 3                       (d) 2

Solution
Speed of boat = 6 km/hr
Speed of stream = y km/hr

Downstream speed = (6 + y) km/hr
Upstream Speed = (6 – y) km/hr

Now
3 * (Distance / Downstream speed) = (Distance / Upstream speed)

3 * (Distance / 6+y) = (Distance / 6-y )

3 * (1/6 + y) = 1/6-y

On solving we get;
y = 3 km/hr

Option (c) is the right answer

Q10. A boat goes 40 km upstream in 8 hours and 36 km downstream in 6 hours. The speed of the boat in still water is

(a) 6.5 km/hr      (b) 5.5 km/hr

(c) 6 km/hr          (d) 5 km/hr