Boats and Streams – Formulas, Aptitude Questions and Answers with Explanation, Tips and Tricks (Solved Examples on Upstream and Downstream)

Formulas and Quick Tricks for Boats and Streams

1. Upstream: In water, the direction against the stream is called upstream.
2. Downstream: In water, the direction along the stream is called downstream.
3. Let the speed of a boat in still water be u km/hr and the speed of the stream be v km/hr, then:
   • Speed downstream = (u + v) km/hr
   • Speed upstream = (u – v) km/hr.
4. Let the speed downstream be a km/hr and the speed upstream be b km/hr, then:
   • Speed in still water =1/2(a+b) km/hr
   • Rate of stream = 1/2(a−b) km/hr
5. A man can row a boat in still water at x km/hr in a stream flowing at y km/hr. If it takes him t hours to row a place and come back, then the distance between the two places = t(x²−y²) / 2x km
6. A man takes n times as long to row upstream as to row downstream the river. If the speed of the man is x km/hr and the speed of the stream is y km/hr, then x = y(n+1) / (n−1)

Questions and Solved Examples on Boats and Streams

Q.1: A boat takes 28 hours for travelling downstream from point A to point B and coming back to point C midway between A and B. If the velocity of the stream is 6km/hr and the speed of the boat in still water is 9 km/hr, what is the distance between A and B?
A. 115 kms
B. 120 kms
C. 140 kms
D. 165 kms
Answer: B. 120 kms
Explanation:
Downstream speed = 9+6 = 15
Upstream speed = 9-6 = 3
Now total time is 28 hours
If distance between A and B is d, then distance BC = d/2
Now distance/speed = time, so
d/15 + (d/2)/3= 28
Solve, d = 120 kms

Q.2: Speed of a man in still water is 5 km/hr and the river is running at 3km/hr. The total time taken to go to a place and come back is 10 hours. What is the distance travelled?
A. 10 kms
B. 16 kms
C. 24 kms
D. 32 kms
Answer: D. 32 kms
Explanation:
Down speed= 5+3= 8
Up speed= 5-3=2
Let distance travelled = X
(X/8)+(X/2)= 10
X = 16 kms
Total distance is 16+16 = 32 kms


Q.3: A boat running upstream takes 9 hours 48 minutes to cover a certain distance, while it takes 7 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?
A. 5:2
B. 7:4
C. 6:1
D. 8:3
Answer: C. 6:1
Explanation:
Distance covered upstream in 9 hrs 48 min = Distance covered downstream in 7 hrs
(X-Y) 49/5 = (X+Y) 7
X/Y = 1/6

Q.4: A boat can travel 20 km downstream in 24 min. The ratio of the speed of the boat in still water to the speed of the stream is 4 : 1. How much time will the boat take to cover 15 km upstream?
A. 20 mins
B. 22 mins
C. 25 mins
D. 30 mins
Answer: D. 30 mins
Explanation:
Down speed =20/24*60=50km/hr
4:1 =4x:x
Downstream speed = 4x+x=5x
Upstream speed = 4x-x=3x
5x= 50; x=10
so up speed 3*10=30
Time = 15/30*60= 30 mins

Q.5: A boat whose speed in 20 km/hr in still water goes 40 km downstream and comes back in a total of 5 hours. The approx. speed of the stream (in km/hr) is:
A. 6 km/hr
B. 9 km/hr
C. 12 km/hr
D. 16 km/hr
Answer: B. 9 km/hr
Explanation:
Let the speed of the stream be x km/hr. Then,
Speed downstream = (20 + x) km/hr,
Speed upstream = (20 – x) km/hr.
40/20+x + 40/20-x = 5
X = 9 km/hr appx.

Q.6: A boat covers a certain distance downstream in 2 hour, while it comes back in 2 1/2 hours. If the speed of the stream be 5 kmph, what is the speed of the boat in still water?
A. 40 kmph
B. 30 kmph
C. 35 kmph
D. 45 kmph
Answer: D. 45 kmph
Explanation:
Let the speed of the boat in still water be x kmph. Then,
Speed downstream = (x + 5) kmph,
Speed upstream = (x – 5) kmph.
(x + 5)*2 = (x – 5)*5/2
X = 45 kmph

Q.7: A boat running downstream covers a distance of 40 km in 5 hrs and for covering the same distance upstream it takes 10 hrs. What is the speed of the stream?
A. 5 km/hr
B. 2 km/hr
C. 6 km/hr
D. 4 km/hr
Answer: B. 2 km/hr
Explanation:
Downstream speed = 40/5 = 8 km/hr
Upstream speed = 40/10 = 4 km/hr
So speed of stream = 1/2*(8-4)

Q.8: A boat goes 4 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 15 km in stationary water?
A. 2 hours
B. 2 hours 15 mins
C. 3 hours
D. 3 hours 30 mins
Answer: C. 3 hours
Explanation:
Rate downstream = 1/10 * 60 = 6kmph
Rate upstream = 4 km/hr.
Speed in still water = ½ * 10 = 5 kmph
Required time = 15/5 = 3 hours


Q.9: A man rows to a place 40 km distant and come back in 9 hours. He finds that he can row 5 km with the stream in the same time as 4 km against the stream. The rate of the stream is:
A. 1 km/hr
B. 1.5 km/hr
C. 2 km/hr
D. 2.5 km/hr
Answer: A. 1 km/hr
Explanation:
Speed downstream = 5/x
Speed upstream = 4/x
40/(5/x) + 40/(4/x) = 9
X = ½
So, Speed downstream = 10 km/hr, Speed upstream = 8 km/hr
Rate of the stream = 1/2 * 2 = 1 km/hr

Q.10: A man can row 8 km/hr in still water. When the river is running at 4 km/hr, it takes him 2 1/3hr to row to a place and come back. How far is the place?
A. 4 kms
B. 5 kms
C. 7 kms
D. 10 kms
Answer: C. 7 kms
Explanation:
Downstream speed = 8+4= 12 => a
Upstream speed = 8-4= 4 => b
Distance = a*b/(a+b) * total time (t)
= 12*4/16 * 7/3
= 7 kms