**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 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.