In this post, we will learn about boat and stream concept, and provide sample questions to help you understand the topic better.
General Points to Remember
- Water always flows in downward direction.
- Boat can able to travel both upward and downward direction.
- Speed = Distance/Time
- Time = Distance/Speed
- Distance = Speed*Time
- Distance = km/hr*hr
Distance = km - 1km/hr = 1000m/3600sec = 5/18
km/hr*5/18 = m/sec
m/sec *18/5 = km/hr - Downstream Speed: If the boat is moving along with water direction. This is called as Downstream speed.
- Upstream Speed: If the boat is moving against the water direction. This is called as Upstream Speed.
- Speed of water = Speed of Stream = Speed of current
- Speed of boat = Speed of man
- Speed of boat = Speed of boat in still water = Speed of boat in normal water
- Rate = velocity = speed
- D1/S1 + D2/S2 = T
- Speed is inversely proportional to time
S1:S2 = 3:4
T1:T2 = 4:3
Problems and Solutions
Q1: If the boat is moving 8km/hr along the current and rate of the current is 1km/hr. Find the speed of the boat is moving against the current and speed of boat in still water?
Solution:Speed of boat in still water = Downstream speed – water speed
Speed of boat in still water = 8-1
Speed of boat in still water = 7 km/hr
Upstream speed = Speed of Boat – water speed
Upstream speed = 7-1
Upstream speed = 6km/hr
Q2: Man move 20km/hr against the stream and reform the same distance in 28km/hr. Find the speed of the man in still water and rate of the current?
Solution:Speed of man in still water = (Up+Down)/2
Speed of man in still water = (20+28)/2
Speed of man in still water = 24km/hr
Speed of stream = (Down-up)/2
Speed of stream = (28-20)/2
Speed of stream = 4km/hr
OR Water speed = DS-US/2
1 = 8-US/2
US = 8-2
US = 6km/hr
Boat speed = DS+US/2
Boat speed = 8+6/2
Boat speed = 7km/hr
Q3: If the speed of boat in still water is 10km/hr and rate of current is 3km/hr. Find the speed of boat along the current?
Solution:Speed of boat along current = Boat speed + Water speed
Speed of boat along current = 10+3
Speed of boat along current = 13km/hr
Speed of Boat against the current = Boat Speed – Water Speed
Speed of Boat against the current = 10-3
Speed of Boat against the current = 7km/hr
Q4: A man swims downstream 30 km and upstream 18km, Taking 3hrs each time, water is the velocity of current?
Solution:Man's rate downstream = 30/3km/hr
Man's rate downstream = 10km/hr
Man's rate upstream = 18/3km/hr
Man's rate upstream = 6km/hr
velocity of stream = 10-6/2
velocity of stream = 2km/hr
Q5: A man moves 100km downstream in 4hrs and return the same distance in 5hrs. Find the total time taken to cover the distance?
Solution:T = D1/S1 + D2/S2
S1 = 100/4 = 25km/hr
S2 = 100/5 = 20km/hr
T = 100/25 + 100/20
T = 4+5 = 9hrs
Q6: A boat moves along the stream with a speed of 40km/hr and return the same distance in 30km/hr. The total time taken to cover the entire journey is 7hrs. Find the total distance travelled?
Solution:T = D1/S1 + D2/S2
7 = x/40 + x/30
7 = (3x+4x)/120
x = 120km
Total Distance = 120 + 120 = 240km
Q7: Ramesh can row a certain distance in 6hrs and return the same distance in 9hrs. If the stream flows at the rate of 3 km/hr. Find the speed of ramesh in still water?
Solution:T1:T2 = 6:9
T1:T2 = 2:3
S1:S2 = 9:6
S1:S2 = 3:2
1R = 3km/hr
Speed of ramesh in still water is 5R = 5*3 = 15km/hr
OR Ramesh speed in still water = Water speed * (t1+t2)/t2-t1
Ramesh speed in still water = 3*(9+6)/(9-6)
Ramesh speed in still water = 15km/hr
Q8: Kubera can row a certain distance Downstream in 6hrs and return the same distance in 9hrs. Speed of kubera in still water is 15km/hr. Find the speed still water is 15 km/hr. Find the speed of the stream?
Solution:T1:T2 = 6:9 = 2:3
S1:S2 = 3:2
5R = 15km/hr
1R = 3km/hr
Speed of Stream = 3km/hr
OR Speed of Stream = man speed*(t2-t1)/(t1+t2)
Speed of Stream = 15*(9-6)/(9+6)
Speed of Stream = 3km/hr
Q9: Shiva can row 6km/hr in still water it takes him twice as long to row up as to row down the river. Find the rate of stream?
Solution:Man's rate in upstream = x km/hr
Man's rate in downstream = 2x km/hr
Man's rate in still water = x+2x/2 = 6km/hr
x = 4km/hr, 2x = 8km/hr
Rate of Stream = 8-4/2 = 2km/hr
Q10: Lakshmi travels downstream 400km with a speed of 100km/hr and return the certain distance with a speed of 80km/hr. The total time taken to cover the whole journey is 8hrs. Find the return journey distance?
Solution:D1/S1 + D2/S2 = T
400/100 + x/80 = 8
x/80 = 4
x = 320km
Q11: A surya can row 6 km/hr in still water when the river is running at 1.2 km/hr, it takes him 1hr to row to a place and back. How far is the place?
Solution:Let the required distance be 'x' km
x/7.2 + x/4.8 = 1
x = 7.2*4.8/12 = 2.88km
OR Required distance = Time*(Boatspeed2-water speed2)/DS+US Required distance = 1*(62-1.22)/12
Required distance = 2.88km
Q12: A boat covers 24km upstream and 36km downstream in 6hrs. While it covers 36 km upstream and 24km down streams in 6.5hrs. Find the velocity of current?
Solution:Upstream speed = 24*24-36*36/24*6-36*6.5
US DS Time 24 36 6 36 24 6.5
Upstream speed = 12 km/hr
Speed of current = 12-8/2 = 2 km/hr
Q13: A boy can swim in still water at 4.5km/hr, but takes twice as long to swim upstream than downstream. The speed of the stream?
Solution:Speed of boy = 4.5 km/hr
Let Speed of stream =x km/hr
Downstream Speed = 4.5 + x
Upstream Speed = 4.5 - x
Distance is
4.5+x = (4.5-x)/2
x = 1.5km/hr
Q14: A motor boat takes 12hrs to go down stream and it takes 24hrs to return the same distance. What is the time taken by boat in still water?
Solution:If t1 and t2 are the upstream and downstream time. Then time taken in still water is given by
= 2*t1*t2/t1+t2
= 2812*24/12+24
= 16hrs.
Q15: A man moves 4km against the stream in 24 minutes and return the same distance in 20 minutes. Find the speed of man in still water and rate of the stream?
Solution:Upstream speed = 4km/ 24/60
Upstream speed = 4*60/24
Upstream speed = 10km/hr
Downstream speed = 4km/ 20/60
Downstream speed = 4*60/20
Downstream speed = 12 km/hr
Speed of man in still water = 11km/hr
Rate of stream = 1 km/hr
Q16: A man can row against the current three fourth of a kilometer in 15min and return the same distance in 10min, then ratio of his speed to that of current?
Solution:let the speed of men in still water = x km/hr
Speed of current = y km/hr
Now, According to the question
(x+y) * 10 = (x-y)*15
10x + 10y = 15x – 15y
5x = 25y
x=5y
x:y = 5:1
K. Mahesh
Aptitude Trainer