This material
prepared and compiled by Akula. Praveen Kumar, SPM, Papannapet Sub Office502
303, Medak Division, Andhra Pradesh (9849636361, 8019549939)
Disclaimer:
All questions/Information provided in this post are Compiled by A. Praveen
Kumar for in good faith of Departmental Employees. The types of questions,
number of questions and standard of questions may be vary in actual
examination. This is my predictions only. Author of blog does not accepts any
responsibility in relation to the accuracy, completeness, usefulness or
otherwise, of the contents.
BOATS AND STREAMS
1.When a boat is
moving in the same direction as the stream or water current, the boat is said
to be moving with the stream or moving downstream.
2.Instead of boats in
water, it could be a swimmer or a cyclist cycling against or along the wind.
3. When a boat is
moving in a direction opposite to that of the stream or water current, the boat
is said to be moving against the stream or water current or moving downstream.
4. When the speed
of the boat is given, it is the speed of the boat in still water.
5. Speed of the
boat against stream or while moving upstream = Speed of the boat in still water
 Speed of the stream.
6. Speed of the
boat with stream or while moving downstream= Speed of the boat in still water +
Speed of the Stream.
7. If 'p' is the
speed of the boat down the stream and 'q' is the speed of the boat up the
stream, then,
Speed of the boat
in still water = (p+q) / 2.
Speed of the boat
of the water stream = (pq) / 2.
8.These problems are governed by the following results:
Downstream
(along the current) speed (D) = Boat speed (B) + current (stream) speed (C).
D=B+C
Upstream
(against the current) speed (U) = Boat speed – current (stream) speed. U=B–C
Speed
of the boat = average of downstream and upstream speeds B = (D + U)/2
Speed
of the current = half the difference of downstream and upstream speeds
C = (D – U)/2
Example:
1.A boat takes 5 hours to go from A to B and 8 hours to return
to A. If AB distance is 40 km, find the speed of (a) the boat and (b) the
current.
Sol: Since B to A takes more
time, it is upstream and hence AB is downstream. Downstream speed = 40/5 = 8
kmph.
Upstream speed= 40/8 = 5 kmph.
Boat speed = (8 + 5)/2 = 6.5 kmph.
Current speed = (8 – 5)/2 = 1.5 kmph.
2.A man cn row a boat at 20 kmph in still water.If the speed of the
stream is 6 kmph, what is the time taken to row a distance of 60 km downstream
?
Sol: Speed of
downstream = boat speed + stream speed = 20 + 6 = 26
kmph
Time required to cover 60 km downstream = d/s = 60/26 = (30/13) hours.
3.The time
taken by a man to row his boat upstream is twice the time taken by him to row
the same distance downstream. If the speed of the boat in still water is 42
kmph, find the speed of the stream ?
Sol: The time taken to row
his boat upstream is twice the time taken by him to row the same distance
downstream. Therefore, the ratio of the time taken is (2:1). So, the ratio of
the speed of the boat in still water to the speed of the stream = (2+1)/(21) =
3:1 .Thus, Speed of the stream = (42)/3 = 14 kmph.
4. A boat travels 36 km upstream in 9 hours and 42 km downstream in 7 hours.
Find the speed of the boat in still water and the speed of the water current ?
Sol: Upstream speed of the boat = 36/9
= 4 kmph
Downstream speed of
the boat = 42/ 7 = 6kmph.
Speed of the boat in
still water = (6+4) / 2.
= 5 kmph
Speed of the water current
= (64) /2
= 1 kmph
5.A man can row at 10 kmph in still water. If it takes a total of 5 hours
for him to go to a place 24 km away and return, then find the speed of the
water current ?
Sol: Let the speed of the water
current be y kmph.
Upstream speed = (10
y) kmph
Downstream speed =
(10+y) kmph
Total time = (24/
10+y) + ( 24/10y) = 5
Hence, 480/ (100y2 )
= 5
480= 5005y2, 5y2= 20
y2= 4, y = 2 kmph.
6.A man can row x kmph in still waters. If in a stream which is flowing at
y kmph, it takes him z hrs to row from A to B and back (to a place and back),
then
Sol: The distance between A and B = z ( x2  y2) / 2x.
7. A man can row 6 kmph in still water. When the river is running at 1.2
kmph, it takes him 1 hour to row to a place and back. How far is the place?
Sol: Required distance = 1 x ( 62  (
1.2)2) kmph
= (36  1.44) / 12
= 2.88 km.
In the above case, If
distance between A and B, time taken by the boat to go upstream and back again
to the starting point, speed of the stream are given; then the speed of the
boat in still waters can be obtained using the above given formula.
8. A man rows a certain distance downstream in x hours and returns the
same distance in y hrs. If the stream flows at the rate of z kmph then,
Sol: The speed of the man in still water = z(x+y) / ( yx) kmph.
9.Ramesh can row a certain distance downstream in 6 hours and return the
same distance in 9 hours. If the stream flows at the rate of 3 kmph. Find the
speed of Ramesh in still water?
Sol: Ramesh's speed in still water = 3
(9+6) / (96)
= 15 kmph.
10.A man rows a certain
distance downstream in x hours and returns the same distance in y hours. If the
speed of the man in still water z kmph, then
Sol: Speed of the stream = z (yx) / (x+y) kmph.
11. Abhinay can row a certain distance downstream in x hours and returns the same
distance in y hours. If the speed of Abhinay in still water is 12 kmph. Find the speed of the stream?
Sol: Speed of the stream = 12 ( 96) / (9+6)
= 2.4 kmph.
12. If a man can
swim downstream at 6 kmph and upstream at 2 kmph, his speed in still water is
Speed in still water = (1/2) * (6 + 2) km/hr = 4 km/hr
13.If a boat goes
7 km upstream in 42 minutes and the speed of the stream is 3 kmph, then the
speed of the boat in still water is
Sol: Rate
upstream = (7/42)*60 kmh = 10 kmph. Speed of stream = 3 kmph.
Let speed in sttil water is x km/hr
Then, speed upstream = (x —3) km/hr.
x3 = 10 or x = 13 kmph.
Let speed in sttil water is x km/hr
Then, speed upstream = (x —3) km/hr.
x3 = 10 or x = 13 kmph.
14. A man rows 13
km upstream in 5 hours and also 28 km downstream in 5 hours. The velpciy of the
stream is
Sol: speed
upstream = (13/5) kmph
speed downstream (28/5) kmph
Velocity of stream = (1/2)[(28/5)  (13/5)] = 1.5 kmph
speed downstream (28/5) kmph
Velocity of stream = (1/2)[(28/5)  (13/5)] = 1.5 kmph
15. A man can row
a boat at 10 kmph in still water. If the speed of the stream is 6 kmph, the
time taken to row a distance of 80 km down thestream is
Sol; Speed
downstream (10+6) km/hr 16 km/hr.
Time taken to cover 80 km downstream = (80/16) hrs = 5 hrs
Time taken to cover 80 km downstream = (80/16) hrs = 5 hrs
16.A man can row 9 and 1/3 kmph 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
Sol: Let speed upstream is x
kmph.
Then, speed downstream = 3x kmph. Speed in still water = (1/2)(3x + x) kmph = 2x kmph. 2x = 28/3 x = 14/3 Speed upstream = 14/3 km/hr, Speed downstream 14 km/hr. speed of the current = (1/2)[14  (14/3)] = 14/3 = 4 and 2/3 kmph 
17.A man rows 750
m in 675 seconds against the stream and returns in 7 and half minutes. His
rowing speed in still water is
Sol: Rate
upstream = (750/675) = 10/9 m/sec
Rate downstream (750/450) m/sec = 5/3 m/sec.
Rate in still water = (1/2)*[(10/9) + (5/3)] m/sec. = 25/18 m/sec
= (25/18)*(18/5) kmPh = 5 kmph
Rate downstream (750/450) m/sec = 5/3 m/sec.
Rate in still water = (1/2)*[(10/9) + (5/3)] m/sec. = 25/18 m/sec
= (25/18)*(18/5) kmPh = 5 kmph
18.If anshul rows
15 km upstream and 21 km downstream taking 3 hours each time, th’en the speed
of the stream is : .
Sol: Rate
upstream = (15/3) kmph
Rate downstream (21/3) kmph = 7 kmph.
Speed of stream (1/2)(7  5)kmph = 1 kmph.
Rate downstream (21/3) kmph = 7 kmph.
Speed of stream (1/2)(7  5)kmph = 1 kmph.
19.A man rows to a place 48 km
distant and come back in 14 hours. He finds that he can row 4 km with the
stream in the same time as 3 km against the stream. The rate of the stream is:
Sol:
Suppose
he move 4 km downstream in x hours. Then,
Speed downstream =


4


km/hr.

x

Speed upstream =


3


km/hr.

x


48

+

48

= 14 or x =

1

.

(4/x)

(3/x)

2

So,
Speed downstream = 8 km/hr, Speed upstream = 6 km/hr.
Rate of the stream =

1

(8  6) km/hr = 1 km/hr.

2

20. 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:
Sol:
Let
man's rate upstream be x kmph.
Then,
his rate downstream = 2x kmph.
(Speed in still water) : (Speed
of stream) =


2x + x


:


2x  x


2

2

=

3x

:

x

2

2

= 3 : 1.
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