Aptitude for CAT, GMAT , Bank Tests, Campus Placements
Solved problems on
Boats and Streams:
1.
If the speed
of a boat in still water is 14 kmph and the rate of stream is 4 kmph. Find the
upstream speed and downstream speed of the boat?
a)10 kmph & 18 kmph b)18
kmph & kmph
c)16 kmph & 8 kmph d)7
kmph & 12 kmph
Answer
: A
Explanation
:
Given that speed of boat x= 14 kmph
Speed of stream y= 4 kmph
$\therefore$ Upstream speed = (x -
y) = 14 -4 = 10 kmph
$\therefore$ Downstream speed = (x + y)=
14+4 = 18 kmph
2.
The speed of
man in still water is 12 kmph. What will be his speed with the stream, if his
speed in upstream is 8 kmph?
a)
9 kmph b)
11 kmph c)14 kmph d)16 kmph
Answer:
D
Explanation:
Given
that, speed of the man in still water= 12 kmph
Upstream speed of the man (x-y)=8 kmph
=>(12-y)=8
$\therefore$ speed of the stream
y=4 kmph
Speed downstream =(x+y)=(12+4)= 16 kmph
3.
Sharma can row
upstream at 14 kmph and downstream at 8 kmph. Find the Sharma’s rate in still
water and the speed of the current?
a)11kmph , 3 kmph b)12
kmph,6 kmph
c)11 kmph, 6 kmph d)14 kmph , 5 kmph
c)11 kmph, 6 kmph d)14 kmph , 5 kmph
Answer
: A
Explanation
:
According
to formula (4),Speed of Sharma in still water =$\frac{(Downstream\:Speed\:+Upstream\:Speed)}{2}$
=
$\frac{1}{2}$ (14+8) = $\frac{22}{2}$ = 11 kmph
Speed of the current = $ \frac{(Downstream\:Speed\:- Upstream\:Speed)}{2}$
=$ \frac{1}{2}$
(14-8)
= $\frac{6}{2}$ = 3 kmph
4.
A man can
row 40 km downstream and 24 km upstream, taking 8 hours each time. What Is the
speed of the stream?
a)1 kmph b)1.5 kmph c)2 kmph d)2.5
kmph
Answer
: A
Explanation
:
Speed downstream = $\frac{Distance}{Time}$ = $\frac{40}{8}$ = 5 kmph
Speed Upstream = $ \frac{Distance}{Time}$ = $\frac{1}{2}$ = 3 kmph
Speed downstream = $\frac{Distance}{Time}$ = $\frac{40}{8}$ = 5 kmph
Speed Upstream = $ \frac{Distance}{Time}$ = $\frac{1}{2}$ = 3 kmph
Speed of the stream =
$ \frac{(Downstream\:Speed\:- Upstream\:Speed)}{2}$
= $\frac{1}{2}$
( 5-3) = 1
kmph
5.
A boat rows
2 km in 10 minutes along the stream and 12 km in 2 hours against the stream.
Find the speed of the stream?
a)
9 kmph b)3
kmph c)6
kmph d)12 kmph
Answer : B
Explanation:
Let
the speed of boat and current be x and y kmph.
Upstream
speed =(x-y) kmph and Downstream speed=(x+y) kmph
Boat rows 2 km in 10 minutes along the stream=>
Downstream speed= $ \frac{Distance}{Time}$= $ \frac{2}{10/60}$ = 12 kmph
Boat rows 12 km in 2 hours against the stream=>
Upstream speed= $ \frac{Distance}{Time}$ = $\frac{12}{2}$ = 6 kmph
Boat rows 2 km in 10 minutes along the stream=>
Downstream speed= $ \frac{Distance}{Time}$= $ \frac{2}{10/60}$ = 12 kmph
Boat rows 12 km in 2 hours against the stream=>
Upstream speed= $ \frac{Distance}{Time}$ = $\frac{12}{2}$ = 6 kmph
Downstream speed (x+y)= 12 kmph
Upstream speed (x-y)= 6 kmph
On solving 1 and 2, we get x=9 kmph and y=3
kmph.
$\therefore$ speed of the stream = 3 kmph
6.
A man rows 4
km in 30 minutes along the stream and 1 km in 30 minutes against the stream. Find
the speed of man in still water?
a)
3 kmph b)5
kmph c)7
kmph d)8 kmph
Answer: B
Explanation:
Let
the speed upstream be x kmph and speed downstream be y kmph.
Man
rows 4 km in 30 minutes along the stream=>
Downstream speed=> (x + y)= $\frac{4}{\frac{30}{60}}$ = $ \frac{4}{\frac{1}{2}}$
= 8 kmph
Man
rows 1 km in 30 minutes against the flow
=>
Upstream speed=>(x-y)=$ \frac{1}{\frac{30}{60}}$
=$ \frac{1}{\frac{1}{2}}$
= 2 kmph
Speed
of the man in still water= $\frac{(Downstream\:Speed\:+Upstream\:Speed)}{2}$
=$\frac{(8+2)}{2}$
= 5 kmph.
7.
What time
will be taken by a boat to travel a distance of 60 km in downstream, if speed
of boat in still water is 15 kmph and velocity of current is 5 kmph?
a)1.5 hours b)2
hours c) 2.5 hours d)3
hours
Answer:
D
Explanation
:
Given that, Speed of boat in still water = 12 kmph
Speed of
stream (Velocity of current) = 5 kmph
$\therefore$ Downstream
speed of boat = (x + y ) = 15 +5 = 20
kmph
Time
taken by boat to travel 60 km in downstream= $\frac{Distance}{Downstream\:Speed}$
= 60/20 = 3 hours
8.
A boat can
row 9 kmph in still water. It takes him twice as long as row up as to row down
the river. Find the speed of the current?
a)
2 kmph b)2.5 kmph c)3 kmph d)4 kmph
Answer:
C
Explanation
:
Let speed of the boat in still water be x and
speed of the current be y.
Given that Upstream time= 2 x
Downstream time
Downstream speed = 2 x Upstream speed
x + y ) = 2 ( x – y )
=> 9 + y
= 2 ( 9 – y )
=> 3y= 9
Speed of the current =
3 kmph.
9.
A man can
row 12 kmph in still water and speed of the stream is 6 kmph. It takes 1 hour
to row to a place and to come back. How far is the place?
a)4.5 km b)5 km c)5.2
km d)5.8
km
Answer
: A
Explanation
:
Let the distance
be D.
Speed of the man in still water = 12 kmph
Speed of the stream =6
kmph
Man’s downstream speed (x + y)=
12+6 = 18 kmph
;Man’s upstream speed (x - y) = 12-6 = 6 kmph
Given that time take to cover both the downstream and upstream is 1 hour.
T1 + T2 = 1 hour
$ \frac{D}{USS}$
+ $ \frac{D}{DSS}$
= 1 hour
$\frac{D}{6}$ + $\frac{D}{18}$
= 1
$\frac{4D}{18}$ = 1
D=$\frac{18}{4}$ = 4.5 km
$\therefore$ the distance = 4.5 km
10. A boat can row a certain distance downstream in 16 hours
and can return the same distance in 24 hours. If the stream flows at the rate
of 6 kmph, find the speed of the man in still water?
a)
36 kmph b)38 kmph c)42 kmph d)50
kmph
Answer
: C
Explanation
:
Let
the speed of boat in still water = x . Speed of stream y=8 kmph
Boat’s downstream speed = (x+6) Boat’s upstream speed =(x-6)
Distance = Speed x Time
Distance = Upstream speed x 24 hours Distance = Downstream speed x 16 hours
= ( x – 6 ) x 24 = ( x + 6 )
x 18
24(x-6)=
18(x+6)
24x - 144 = 18x+ 108
6x = 252
X = 42
Speed
of boat in still water = 42 kmph
11. Speed of a man in still water is 12 kmph while river is flowing
with a speed of 4 kmph and time taken to cover a certain distance upstream is 6
hours more than time taken to cover the same distance downstream. Find the distance?
a)
90 km b)96
km c)84 km d)108 km
Answer
: B
Explanation
:
Let
distance be D .
Given
that speed of man in still water x=12
and speed of stream = 4 kmph
His upstream speed =(x-y)= 12-4 =8 kmph
Downstream speed (x+y)= 12+4 = 16
kmph
Given that
$\frac{D}{USS}$ – $\frac{D}{DSS}$
= 6 hours
ð $\frac{D}{8}$
– $\frac{D}{16}$ = 6
ð $\frac{2D - D}{16}$ = 6
ð D=96
km
$\therefore$
the distance covered is 96 km
12. A steamer goes downstream from one port to another in 4 hours
.It covers the same distance upstream in 5 hours. If the speed of the stream is
2 kmph, find the distance between the
two ports ?(Staff Selection Commission 2007
SSC Previous Question 2007)
a)
50 km b)60 km c)70 km d)80 km
Answer : D
Explanation :
Let
the distance between two ports = D
The downstream speed = $\frac{D}{4}$
Upstream speed = $\frac{D}{5}$
Given that speed of the stream is
2 kmph
Speed of the stream = ½(DSS –
USS) = 2
=
$\frac{1}{2}$ ( $\frac{D}{4}$ – $\frac{D}{5}$) =2
=>$\frac{5D - 4D}{20}$ = 4
=> D = 80
$\therefore$ the distance
between two ports = 80 km
13. The speed of a motor boat is 30 kmph. It starts from Kakinada
port at 8 a.m and reaches Vizag port at 11 a.m . Same day it starts from Vizag
port at 12 p.m and reaches Kakinada port at
6 p.m. Find the distance between Kakinada and Vizag and find the speed
of the stream?
a)
80 KM b)120km c)145 km d)180
km
Answer
: B
Explanation
:
Given
that boat takes 3 hours to go from Kakinada to Vizag and 6 hours to go from
Vizag to Kakinada.
Let speed of the stream be y
Time in Upstream = 2 x Time
in downstream
ð Downstream
speed = 2 x Upstream speed
ð (30 + y)= 2(30-y)
ð 3y
=30 => y = 10 kmph
$\therefore$, Speed of the stream = 10 kmph
Downstream Speed = (x + y) = 30+10 = 40 kmph
Distance between Vizag and Kakinada =
Downstream Speed x Time taken in downstream
= 40 kmph x 3 hours = 120 km
14. In a river, the ratio of the speeds of the boat in still water
and the speed of the stream is 7:3. Again , ratio of the speed of an another
boat in still water and speed of the stream is 9:2. What is the ratio of the
speeds of the first boat to the second boat in still water?
a)
7:6 b)7:5 c)6:7 d)8:5
Answer
: A
Explanation
:
For the first boat, Speed of the boat in still
water : Speed of stream = 7 :3
Then
Speed of boat in still water =7x and speed of stream =3x
Similarly,
for the second boat, speed of the boat in still water = 9y and speed of the
stream = 2 y
River is same in both conditions, then
speed of stream in both cases is equal
ð 3x
=2y=> x=$\frac{3}{2}$ y
Now, the required ratio of speeds of
boats = 7x: 9y
ð 7
x $\frac{3y}{2}$ : 9y
ð 21y
: 18y
ð 7:6
The ratio of the speeds of first boat in
still water to speed of second boat in still water = 7:6
15. There is a road beside a river. Two men Sudheer and Ravi,
started from a place A , moved to another place B and returned to A again.
Sudheer started moving on a bike at a speed of 14 kmph, while Ravi sails in
boat at speed of 12 kmph. If the speed the river is 3 kmph, which of the two
men will return to place A first?
a)Ravi b)Sudheer c)Both will reach together d)Cant be determined
Answer
: B
Explanation
:
Sudheer
travels on bike both ways at a speed of 14 kmph.
Given
that speed of Ravi in still water is 12 kmph and speed of the stream is 3 kmph.
Ravi
sails his boat in downstream (one way) at (12+3) = 15 kmph and in upstream (another
way) at 12-3=9 kmph.
Average speed of Ravi = $\frac{2ab}{a+b}$ =$\frac{2\times15\times9}{15\dotplus9}
$
=270/24
= 10.12 kmph
Clearly
Speed of Sudheer is 12 kmph and Speed of Ravi is 10.12 kmph
Clearly
Speed of Sudheer > Speed of Ravi.
$\therefore$ Sudheer reaches the place B
first.