Practice Boats and streams - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) A man can row three-quarters of a kilometer against the water stream in $11{1/4}$ minutes and along the stream in $7{1/2}$ minutes respectively. The speed in (km/hr) of the man in still water is
(a)
(b)
(c)
(d)
Q-2) The speed of a boat in still water is 8 km/hr. It can travel 20 km downstream at the same time as it can travel 12 km upstream, the rate of stream (in kmph) is
(a)
(b)
(c)
(d)
Let rate of stream = x kmph
∴ $20/{8+x}=12/{8-x}$
160 – 20x = 96 + 12x
64 = 32x
x = 2
∴ Rate of stream = 2 kmph
Q-3) The speed of a boat in still water is 15 km/h and the rate of stream is 5 km/h. The distance travelled downstream in 24 minutes is
(a)
(b)
(c)
(d)
Downstream speed = 15 + 5 = 20 km/h.
∴ Required distance $20×24/60$=8km
Q-4) 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
(a)
(b)
(c)
(d)
Let speed in downstream = (x + y)
Speed in upstream = (x – y)
∴ (x + y) = 2 (x – y)
x = 3y
x : y = 3 : 1
Q-5) A man rows a distance downstream in 45 min and the same distance upstream in 75 min. What is the ratio of speed of the stream to the boat in still water ?
(a)
(b)
(c)
(d)
Let speed of boat in still water = x km/hr
Let speed of stream = y km/hr
Let distance covered = d km
∴ $d/{x+y}=45/60=3/4$ …(1)
$d/{x-y}=75/60=5/4$ …(2)
Form (1) & (2),
${x-y}/{x+y}=3/5 ⇒5x-5y=3x+3y$
⇒2x=8y ⇒ $y/x=1/4 $
∴ ratio of speed of the stream to boat in still water = 1 : 4
Q-6) A steamer goes downstream from one part to another in 4 hours. It covers the same distance upstream in 5 hours. If the speed of stream is 2 km/hr, the distance between the two ports is
(a)
(b)
(c)
(d)
Let the distance between the two parts = 'x' km
Let the speed of steamer in still water = 'y' km/hr
∴ $x/{y+2}$=4 ⇒x=4y+8 ….(1)
$x/{y-2}$=5⇒x=5y-10 …..(2)
From (1) and (2)
4y+8=5y-10
⇒ y = 18
∴ From (1)
x = 4 × 18 + 8 = 80 km.
Q-7) A boat takes half the time in moving a certain distance downstream than upstream. The ratio between rate in still water and rate of current is
(a)
(b)
(c)
(d)
Let speed of boat in still water = x km/h
speed of current = y km/h
∴ (x + y) × t = (x – y) × 2t
x = 3y
x : y = 3 : 1
Q-8) A man can row 5 kmph in the still water. If the river is running at 2 kmph, it takes him 5 hours to row up to a place and come down. How far is the place?
(a)
(b)
(c)
(d)
Let the distance = d km
Time taken to row upstream '$t_1$ ' = $d/{5-3}=d/2$ …(1)
Time taken to row downstream $'t_2 '$ = $d/{5+3}=d/8$ …(2)
$t_1 + t_2$ = 5 (Given)
∴ $d/2+ d/8 = 5$
⇒ ${4d+d}/8=5⇒ d=8km $
∴ Distance of the place = 8 km.
Q-9) A boat takes 19 hours for travelling downstream from point A to point B and coming back to point C, mid way between A and B. If the velocity of the stream is 4 km/hr and the speed of the boat in still water is 14 km/hr. then the distance between A & B is
(a)
(b)
(c)
(d)
Downstream speed = 14 + 4 = 18 km/hr
Upstream speed = 14 – 4 = 10 km/hr
Let the distance between A and B = 'x' km
∴ $x/18+{x/2}/10=19$
∴ $x/18+x/20=19$
${10x+9x}/180=19$
${19x}/180=19$ ⇒ x=180km
Q-10) A motor boat whose speed is 15 km/h in still water goes 30 km downstream and comes back in four and a half hours. The speed of the stream is :
(a)
(b)
(c)
(d)
Let the speed of the stream be x km/h.
Then, upstream speed = (15 – x) km/h.
and downstream speed = (15 + x) km/h.
Now, $30/{(15 + x)}+30/{ (15 - x)}$ = 4.5
Checking with options, we find that x = 5 km/h.
Q-11) A man can row a boat 120 km with stream in 5 hours. If speed of the boat is double the speed of the stream, then the speed of stream is
(a)
(b)
(c)
(d)
Speed of the boat downstream =$120/5$ = 24 km/h
Ratio of speeds of boat and stream = 2 : 1
∴ Speed of the stream = $1/3×24$ = 8 km/h
Q-12) A man swims downstream 40 km in 4 hours and upstream 24 km in 3 hours. His speed in still water is
(a)
(b)
(c)
(d)
Let speed in downstream = (x + y)
Speed in upstream = (x – y)
∴ 4 (x + y) = 40
x + y = 10 ...(1)
and 3(x – y) = 24
x – y = 8 ...(2)
By (1) and (2)
x = 9, y = 1
∴ speed in still water is 9 km/h
Q-13) A boat goes 24 km upstream and 28 km downstream in 6 hours. It goes 30km upstream and 21 km downstream in 6 hours and 30 minutes. The speed of the boat in still water is :
(a)
(b)
(c)
(d)
Let speed of the boat in still water be x km/h and speed of the current be y km/h.
Then, upstream speed = (x – y) km/h
and downstream speed = (x + y) km/h
Now, $24/{(x-y)}+28/{(x+y)}=6$ …(i)
and $30/{(x-y)}+21/{(x+y)}=13/2$ …(ii)
Solving (i) and (ii), we have
x = 10 km/h and y = 4 km/h
Q-14) A man swimming in a stream which flows 1.5 km/hr, finds that in a given time he can swim twice as fast with the stream as he can against it. At what rate does he swim ?
(a)
(b)
(c)
(d)
Rate of stream = 1.5 km/hr
Let speed of man in still water = u km/hr
and distance = d
∴ downstream speed = (u + 1.5) km/hr
upstream speed = (u – 1.5)km/hr
∴ From question ${2d}/{u+1.5}=d/{u-1.5}$
⇒2u-3=u+1.5
⇒u=4.5 km/hr
Q-15) A person can row a boat d km upstream and the same distance downstream in 5 hours 15 mins. Also he can row the boat 2d km upstream in 7 hours. How long will it take to row the same distance 2d km downstream.
(a)
(b)
(c)
(d)
Let speed in downstream = (x + y)
speed in upstream = (x – y)
∴ $d/{x+y}+d/{x-y}=21/4$ ...(1)
As ${2d}/{x-y}=7$
∴ ${2d}/{x+y}=21/4 ×2-7$
= $7/2$ hours
Q-16) A boat covers 24 km upstream and 36 km downstream in 6 hours, while it covers 36 km upstream and 24 km downstream in $6{1/2}$ hour. The velocity of the current is
(a)
(b)
(c)
(d)
Let upstream rate = x km/hr,
downstream rate = y km/hr
∴ $24/x+36/y=6$ ...(1)
$36/x+24/y=13/2$ ...(2)
Add (1) and (2) , we get
$60{(1/x+1/y)}=25/2 ⇒ 1/x+1/y=5/24$ ...(3)
Subtract (1) from (2)
$12{(1/x-1/y)}=1/2 ⇒ 1/x-1/y=1/24$ ...(4)
Add (3) and (4)
$2/x=6/24⇒x=8$
rom (3) y = 12
∴ Velocity of current = $1/2{(y-x)}=1/2{(12-8)}$=2km/hr
Q-17) A man rows upstream 24 km and downstream 36 km taking 6 hours each. Find the speed of current.
(a)
(b)
(c)
(d)
Let man's rowing speed in still water = x km/hr
Let speed of current = y km/hr
Downstream speed = x + y = $36/6$ = 6 …(1)
Upstream speed = x – y = $24/6$ = 4 …(2)
(1) – (2)
2y = 2 ⇒ y = 1
∴ speed of current = 1 km/hr.
Q-18) A man rows 10 km upstream and back again to the starting point in 55 min. If the speed of stream is 2 km/hr, then the speed of rowing in still water is
(a)
(b)
(c)
(d)
Let speed in still water = x km/h
Speed of stream = 2km/h
∴ $10/{x+2}+10/{x-2}=55/60$
$10x+10x=11/12(x^2-4)$
$11x^2-240x-44=0$
x = 22
∴ speed in still water = 22 km/h
Q-19) If a man’s rate with the current is 12 km/hr. and the rate of the current is 1.5 km/hr, then man’s rate against the current is –
(a)
(b)
(c)
(d)
Let the rate against the current be x km/hr. Then,
${12-x}/2$ = 1.5 ⇒12 – x = 3 ⇒ x = 9 km / hr
Q-20) The speed of a motor boat to that of the current of water is 36 : 5. The boat goes along with the current in 5 hours 10 minutes. It will come back in
(a)
(b)
(c)
(d)
Let speed of boat = 36x km/h
Speed of current = 5x km/h
∴ $(36x + 5x) × 310/60=(36x-5x) × t$
$t={41×310}/{60×31}=41/6$= 6H 50 min