Boat & Stream - Quantitative Aptitude Questions and Answers
This section focuses on "Boat and Stream" of Quantitative Aptitude. These Multiple Choice Questions (mcq) should be practiced to improve the Quantitative Aptitude skills required for various interviews (campus interviews, walk-in interviews, company interviews), placements, entrance exams and other competitive examinations.
1. A boat takes 27 hrs to travel a distance upstream and takes 9hrs to travel the same distance downstream.
If the speed of the boat in still water is 12km/hr, then what is the velocity of the stream?
Explanation: Let the velocity of the stream be y km/hr
Then the speed of the downstream = (12 + y)km/hr
The speed of the upstream = (12 – y)km/hr
9 (12 + y) = 27 (12 – y)
108 + 9y = 324 – 27y
27y + 9y = 324 - 108
36y = 216
y = 6 km/hr
2. A boat covers 12 km upstream and 18km downstream in 3hrs while it covers 18 km upstream and 12km
downstream in 3(1/4) hrs the velocity of the the boat upstream and downstream?
Explanation: Let rate of upstream be 'x'km/hr and downstream be 'y' km/hr
Then, 12/x + 18/y = 3 -->1
18/x + 12/y =13/4 -->2
Adding 1 and 2 we get,
30/x + 30/y = 25/4
1/x + 1/y +=5/24 -->3
Subtracting 1 and 2 we get
1/x – 1/y = 1/24 -->4
Adding 3 and 4 we get,
2/x = 6/24 ; x= 8 ->5
Substitute 5 in 3 we get, y=12
Speed of upstream = 8 km/hr and downstream = 12 km/hr
3. If a boy rows 8 km downstream in 6 hours and 4 km upstream in 4 hours then how long
will he take to cover 16 km in stationary (still) water?
Explanation: Distance covered in downstream = 8 km
Time taken in downstream = 6 hours.
Rate of downstream = 8/6=4/3 km/hr
Distance covered in upstream = 4 km
Time taken in upstream = 4hours.
Rate of upstream = 4/4 = 1 km/hr
Speed in still water = (1/2)(4/3+1) = 7/6km/hr
Time Taken to cover 16 km in still water = 16*6/7=14hrs (approximately)
4. A boat takes 24 hours to cover 128 km downstream and 16 hours to cover 64 km upstream. Then the speed of the boat in still water is:
Explanation: Distance covered in downstream = 128km
Time taken in downstream = 24 hours.
Rate of downstream = distance / time = a = 128 km /24 hours = 16/3km/hr
Distance covered in upstream = 64km
Time taken in upstream = 16 hours.
Rate of upstream = distance / time = b = 64km /16hours = 4 km/hr.
Speed in still water = (a + b) / 2 = (1/2)(16/3+4) km/hr = (1/2)(28/3)km/hr
5. A pedal boat goes 12km upstream and 14km downstream in 3hrs. It goes 15km upstream and 10.5km
downstream in 3 hrs 15mints. The speed of the boat in still water is:
Explanation: Let 'x' be the speed of the boat in still water
Let 'y' be the speed of the current.
Pedal boat will travel downstream at (x + y)km/hr and upstream (x – y)km/hr
Therefore 14/x +y + 12/ x –y = 3
10.5/(x+y) + 15/(x-y) = 13/4
70/(x+y) +60 /(x-y) =15 -->1
42 /(x+y) + 60/(x-y) = 13 -->2
From 1 and we get,
x+y = 14 ; x-y = 6
Therefore x= 10 ; y = 4
The speed of the pedalboat is 10 km/hr
6. A boatman can take the same time to row6.5km downstream and 3.5km upstream. His
speed in still water 2.5 km/hr. The speed of the stream is:
Explanation: Given that the speed in still water = 2.5 km/hr
Let the speed of the stream be 'x' km/hr
speed in upstream = (2.5 – x)km/hr
Then time taken to cover 6.5 km downstream = 6.5 / (2.5+x)
Then time taken to cover 3.5 km upstream = 3.5 / (2.5 – x)
6.5 / (2.5 + x) = 3.5 / (2.5 – x)
6.5 (2.5 – x) = 3.5 (2.5 + x)
16.25 – 6.5x = 8.75 + 3.5x
10 x = 7.5
x = 0.75 km/hr
The speed of the stream is 0.75 km/hr
7. A woman rows to a place 24km distant and come back in 7 hrs. She finds that she can
row 2km with the stream in the same time as 1.5km against the stream. The rate of the
Explanation: Suppose she move 2km downstream in x hrs
Then, speed of downstream = (2/x) km/hr
Speed of upstream = (1.5/x) km/hr
Therefore 24/(2/x) + 24/(1.5/x) = 7
12x + 16x = 7
X = (1/4)
So speed of downstream = 8km/hr and upstream = 6km/hr
Rate of the stream = (1/2) (8 - 6 )km/hr
= 1 km/hr
8. A girl can row 15 kmph in still water and he finds that it takes him thrice as long to row up as to row down
the river. Find the rate of stream.
Explanation: Given that, time taken to travel upstream = 3 × time taken to travel downstream
When distance is constant, speed is inversely proportional to the time
Hence, 3 × speed upstream = speed downstream
Let speed upstream =x
Then speed downstream =3x
we have, 1/2(x+3x) = speed in still water
i.e., 2x =15 -> x=7.5
i.e., speed upstream =7. 5 km/hr
Rate of stream =1/2(3x−x)= x = 7.5km/hr
9. A fisherman rows to a place 24km distance and back in 7 hours. He finds that he can row 2km with the
stream in the same time 1.5 km against the stream.The rate of the stream is?
Explanation: Let be moves 2 km downstream in x Hours
Then in speed downstream = 2/x kmph
Speed in upstream = 1.5/x kmph
==> 24/2/X + 24/1.5/X = 7
Speed in downstream = 8 Kmph
Speed in upstream = 6 Kmph
Then the Rate of stream = 1/2 (8 - 6) = 1 Kmph
10. A boat goes 3.5km upstream in 24 mins and the speed of the stream is 1.5km per hour,
then the speed of the boat in still water is.
Explanation: Speed of upstream = 3.5 / 24 km/min
= 3.5 / 24 * 60 km/hr
= 8.75 km/hr
Speed of the stream = (1/2) (a – b)km/hr = 1.5 km/hr
1.5 = (1/2) ( a- 8.75)km/hr
a = 11.75 km/hr
speed of the boat in still water = (1/2)(a + b) km/hr
= (1/2) (11.75 + 8.75)
The speed of the boat in still water = 10.25 km/hr
11. A boat man lakes 5hrs 30 mins to row a boat 30km downstream of a river and 4 hrs
15mints to cover a distance of 10km upstream. Find the speed of the river current in km/hr.
Explanation: Rate downstream = 30 / (11/2) km/hr
= 30 * 2 / 11 km/hr
= 60/11 km/hr
Rate upstream = 10 / (17/4)km/hr
= 10 * 4 / 17 km/hr
= 40 / 17 km/hr
Speed of current = 1 / 2 (a – b) km/hr
=1 / 2 (60 / 11 – 40 / 17)
= 1.5 km/hr (approx.)
12. A man can row 4 km against the stream in 40mins and return in 36mins. Find the rate of current.
Explanation: Speed of the man (upstream) = (4 / 40 * 60) km/hr
= 6 km/hr
Speed of the man (downstream) = ( 4 / 36 * 60) km/hr
= (60 / 9)km/hr
= 20/3 km/h
Rate of the current = ½[downstream speed – upstream speed]
= (1/2) [ 20 / 3 – 6] km/hr
Rate of the current = 1/3 km/hr
13. Sakthi rows a boat at 4 km upstream in 1hour and 1 km downstream in 20 minutes.
How long will he take to reach 3.5km in still water?
Explanation: Upstream Speed = 4/1 = 4km/hr
Downstream Speed = 1/20 = 0.05 km/min
= 0.05*60 = 3 km/hr
Hence, speed of boat = 1/2( Upstream Speed + Downstream Speed)
= 1/2 (4+3)km/hr =3.5 km/hr
Thus, the time required to reach the distance of 3.5 km=DistanceCovered/Speed of boat
= 3.5/3.5km/hr =1 km/hr
14. A motor boat sails 30 km of a river towards upstream in 10hrs. How long will it take to
cover the same distance downstream, if the speed of the current is ½ of the speed of the boat
in still water.
Explanation: Upstream speed = x –y
Downstream speed = x + y
x– y = 30/10 = 3km/hr
Again x = 2y
Therefore x – y = 3
y= 3km/hr ; x = 6km/hr
Therefore x + y = 9 km/hr
Time during downstream = 30/9 = 3.33hrs
15. A man goes 4km upstream of the stream in 2hr and goes 2km downstream of the stream in 20mints. How
long will it take to go 10km in stationary water?
Explanation: Rate downstream = (2/20 * 60) km/hr
= 6 km/hr
Rate upstream = 2 km/hr
Speed in still water = ½(6+2)km/hr
= 4 km/hr
Required time = distance / speed
= (10/4) hrs =(5/2)hrs
= 2hrs 30mins.
16. Mohana can row 80km upstream and 110km downstream in 26 hrs. Also she can 60km upstream and
88km downstream in 20 hrs. Find the speed of the girl in still water and the speed of the current in ratio:
Explanation: Let rate upstream = 'x' km/hr and
Rate downstream = 'y' km/hr
Then 80/x + 110/y = 26 --->1
60/x + 88/y = 20-->2
By solving 1 and 2
y= 11 ; x = 5
Rain in still water = (1/2) (11 + 5) km/hr = 8 km/hr
Rain of current = (1/2) (11 – 50) km/hr = 3 km/hr
The required answer is 8:3
17. A motorboat running upstream takes 4 hrs 24 mins to cover a certain distance, while it takes 2hrs to cover
the same distance running downstream. What is the ratio between the speed of the boat and speed of the
water current respectively?
Explanation: Let the man's rate upstream be 'x' km/hr and downstream be 'y' km/hr
Then distance covered upstream by 4hrs 24mints = distance covered by downstream in 2hrs
(x * 4 2/5) = y *2
22x/5 = 2y
Y = 11x/5
Required ratio = (y+x/2) : (y –x/2)
= 16x/10 : 6x/10
= 16x : 6x
18. A person can swim in water with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, what will be the time taken by the person to go 68 km downstream?
Explanation: Downstream Speed = (13+4) km/hr = 17 km/hr
To travel 68 km downstream.
Time taken = 68/17 = 4 hours
19. In one hour, a boat goes 13 km/hr in the direction of the stream and 7 km/hr against the direction of the stream. What will be the speed of the boat in still water?
Explanation: According to the formula,
Speed of a boat in still water = (1/2) (DownstreamSpeed + UpstreamSpeed)
Speed of boat in still water = (1/2) (13+7) = (1/2) × 20 = 10 km/hr
20. A woman can row upstream at 16 km/hr and downstream at 26 km/hr. What is the speed of the stream?
Explanation: According to the formula,
Speed of the stream = (1/2)(Downstream Speed – Upstream Speed)
Speed of the stream = (1/2)(26-16) = (1/2) × 10 = 5 km/hr