PROBLEMS ON BOATS & STREAMS

QUERY 1

The speed of a boat upstream is 2/3 that of downstream. Find the ratio of speed of boat in still water and to the average speed of boat in downstream and upstream.

A) 24/25
B) 25/24
C) 5/12
D) 12/5

MAHA GUPTA
Speed of a body in still water = (speed downstream + speed upstream)/2

Average speed = [2*(speed upstream*speed downstream)]/(speed downstream + speed upstream)

Now let the speed of the boat downstream = 3 km/h
Therefore its speed upstream = 2/3 of 3 = 2 km/h

Hence the speed of the boat in still water = (3 + 2)/2 = 5/2
And the average speed = (2*2*3)/(3+2) = 12/5

Hence the required ratio = 5/2 : 12/5 = 25 : 24 = 25/24 (option ‘B’)

QUERY 2

A man can row upstream 10 km/h and downstream 20 km/h. Find the man’s rate in still water and rate of the stream.

A) 0 km/h,        5 km/h
B) 5 km/h,        15 km/h
C) 15 km/h,       5 km/h
D) 10 km/h,      5 km/h

MAHA GUPTA
Remember,
Speed of a body in still water = (speed downstream + speed upstream)/2
Speed of the current/stream = (speed downstream – speed upstream)/2

Therefore, man’s rate in still water = (20 + 10)/2 = 15 km/h (option ‘C’)
And rate of the stream = (20 – 10)2 = 5 km/h (option ‘C’)

QUERY 3

A man takes 3 hours 45 minutes to row a boat 15 km downstream of a river and 2 hours 30 minutes to cover a distance of 5 km upstream. Find the speed of the current.

A) 1 km/h
B) 2 km/h
C) 3 km/h
D) 4 km/h

MAHA GUPTA
Speed of the current/stream = (speed downstream – speed upstream)/2

So we need to find the downstream and upstream speeds first

We know, Speed = Distance / Time

Hence, speed of the man downstream = 15/3³⁄₄ = 4 km/h                    (3 hours 45 minutes = 3³⁄₄ hours)
And speed of the man upstream = 5/2¹⁄₂ = 2 km/h                             (2 hours 30 minutes = 2¹⁄₂ hours)

Therefore, Speed of the current = (speed downstream – speed upstream)/2 = (4 – 2)/2 = 1 km/h (option ‘A’)

QUERY 4

A motorboat whose speed is 15 km/h in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream is?

A) 2 km/h
B) 3 km/h
C) 4 km/h
D) 5 km/h

MAHA GUPTA
Let the speed of the stream be x km/h
Then, speed of the motorboat downstream = (15 + x) km/h
and speed of the motorboat upstream = (15 – x) km/h

Therefore time taken downstream = ³⁰⁄_15+x  hours
and time taken upstream = ³⁰⁄_15-x hours

Total time taken = 4 hours 30 minutes = 9/2 hours

Therefore, ³⁰⁄_15+x + ³⁰⁄_15-x = 9/2
=> 9x² = 225
=> x = 5 km/h (option ‘D’) 

QUERY 5

A man can row 9¹⁄₃ km/h in still water and finds that it takes him thrice as much time to row up than as to row down the same distance in the river. The speed of the current is?

A) 3²⁄₃ km/h
B) 4²⁄₃ km/h
C) 5²⁄₃ km/h
D) 6²⁄₃ km/h

MAHA GUPTA
Here we need to know the speed of current, of course we will need speed downstream and speed upstream for that.

Now, let the speed upstream = x km/h
Hence, the speed downstream is = 3x km/h

Speed of the man in still water given; and we know that
Speed of a body in still water = (speed downstream + speed upstream)/2
Therefore, (3x + x) = 9¹⁄₃
=> x = 14/3

Hence speed upstream = 14/3 km/h
And speed downstream = 14/3 × 3 = 14 km/h

Therefore, speed of the current = (speed downstream – speed upstream)/2
= (14 – 14/3)/2
= 14/3 = 4²⁄₃ km/h (option ‘B’)  

QUERY 6

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 stream is?

A) 3 : 1
B) 1 : 3
C) 2 : 4
D) 4 : 2

MAHA GUPTA
Let speed of the man  upstream = x km/h
Then, his speed downstream = 2x km/h

Now, speed of the boat in still water = ^{(speed downstream + speed upstream)}⁄₂
= ^2x+x⁄₂ = ^3x⁄₂

And, speed of the stream = ^{(speed downstream – speed upstream)}⁄₂
= ^2x-x⁄₂ = ^x⁄₂

Therefore the ratio = ^3x⁄₂ : ^x⁄₂
= 3 : 1 ( option ‘A’)

QUERY 7

A man’s speed with the current is 20 km/h and speed of the current is 3 km/h. The Man’s speed against the current will be?

A) 11 km/h
B) 12 km/h
C) 14 km/h
D) 17 km/h

MAHA GUPTA
Man’s speed with the current is 20
It does mean it’s speed of the man in still water + speed of the current

Thus his speed in still water = 20 – 3 = 17

Now man’s speed against the current = His speed in still water – speed of current
= 17 – 3 = 14 km/h (option ‘C’)

QUERY 8

A boat can travel with a speed of 16 km/h in still water. If the rate of stream is 5 km/h, then find the time taken by the boat to cover distance of 84 km downstream.

A) 4 hours
B) 5 hours
C) 6 hours
D) 7 hours

MAHA GUPTA
According to the question
Speed of the boat downstream = 16 + 5 = 21 kmph

We know, Time = distance/speed

Therefore time taken by the boat to cover distance of 84 km downstream = 84/21 = 4 hours (option ‘A’)

QUERY 9

A man can row at 5 km/h in still water. If the velocity of the current is 1 km/h and it takes him 1 hour to row to a place and come back. How far is that place?

A) 0.4 km
B) 1.4 km
C) 2.4 km
D) 3.4 km

MAHA GUPTA
Let the distance of the place be x km

Now, the the speed of the man downstream = 5 + 1 = 6 km/h
And his speed upstream = 5 – 1 = 4 km/h

We know, distance/speed = time
We also know, time taken downstream + time taken upstream = total time taken
Thus, x/6 + x/4 = 1
=> x = 2.4 km (option ‘C’)

QUERY 10

Sahil can row 3 km against the stream in 20 minutes and he can return in 18 minutes. What is rate of current?

A) 1/2 km/h
B) 1/3 km/h
C) 2 km/h
D) 4 km/h

MAHA GUPTA
We know, rate of the current = (speed downstream – speed upstream)/2

Hence we need to know the speed downstream and speed upstream

So speed of Sahil downstream = 3/¹⁸⁄₆₀
= 10 km/h

and speed of Sahil upstream = 3/_²⁰⁄60
= 9 km/h

Therefore, the rate of current = (speed downstream – speed upstream)/2
= (10 – 9)/2 = 1/2 km/h (option ‘A’)