Boat and stream questions are a common topic that is frequently asked in various government exams in the quantitative aptitude section. These questions are based on the principle of relative speed and are used to calculate the speed of a boat or a stream in still water, given the speed of the boat in the downstream or upstream direction.
In this article, we will discuss the boat and stream concept, important formulas, tips to solve questions and provide sample questions to help you understand the topic better. Whether you’re preparing for a government exam or simply want to brush up on your quantitative aptitude skills, this article is a must-read for you.
To fully understand the boats and streams concepts, it’s important to have a solid understanding of Speed, Time and Distance as these concepts are closely related.
Practice Quiz :
Practice Boats and Streams Aptitude Quiz Questions
Boats and Streams Concepts
To solve problems based on boats and streams, one must be familiar with important terms like a stream, upstream, downstream, and still water. Additionally, mastering formulas based on distance, speed, and time is crucial for successfully tackling these problems.
- Stream: Moving water in a river or any other water body.
- Upstream: Moving against the direction of the stream or current.
- Downstream: Moving along the direction of the stream or current.
- Still Water: Water in a river or any other water body that is not flowing or stationary.
Upstream and Downstream Formulas
Upstream and downstream are important concepts in boat and stream problems, and understanding the relevant formulas is crucial for solving related questions.
Speed Upstream = B – S km/hr
Speed Downstream = B + S km / hr
Speed of boat in still water = 0.5 x (D + U) km / hr
Rate of stream = 0.5 x (D – U) km/hr
Sample Questions on Boats and Streams
Q1: A 100 m long train moving at a speed of 60 km/hr passes a man standing on the pavement near a railway track. Find the time taken by the train to pass the man.
Length of the train = 100 m = 0.1 km
Speed of the train = 60 km / hr
So, the time taken by the train to pass the man = time taken to cover 0.1 km at the speed of 60 km/hr
Therefore, time taken by the train to pass the man = 0.1 / 60 hour = (0.1 / 60) x 3600 sec = 6 sec
Q2: How long does a train 1000 m long moving at a speed of 90 km/hr would take to pass through a 500 m long bridge?
Here, the time taken by the train to pass the bridge completely would be the time it takes to cover 1000 + 500 = 1500 m at the speed of 90 km/hr = 90 x (5/18) = 25 m / sec.
Therefore, time required = 1500 / 25 = 60 sec = 1 minute
Q3: A man standing near a railway track observes that a train passes him in 80 seconds but to pass by a 180 m long bridge, the same train takes 200 seconds. Find the speed of the train.
Let the length of the train be L meters.
=> The train covers L meters in 80 seconds and L + 180 meters in 200 seconds, with the same speed.
We know that Speed = Distance / Time.
=> Speed = L / 80 = (L + 180) / 200
=> L / 80 = (L + 180) / 200
=> 2.5 L = L + 180
=> 1.5 L = 180
=> L = 120
Thus, speed of the train = 120 / 80 = 1.5 m / sec
Q4: Two trains 140 m and 160 m long are moving towards each other on parallel tracks with speeds of 40 km/hr and 50 km/hr respectively. How much time would they take to pass each other completely?
Total distance to be covered = 140 + 160 m = 300 m
Relative speed = 40 + 50 = 90 km / hr = 90 x (5 / 18) m / sec = 25 m / sec
Therefore, time taken to pass each other = 300 / 25 = 12 sec
Q5: Two trains 140 m and 160 m long are moving in the same direction on parallel tracks with speeds of 40 km/hr and 50 km/hr respectively. How much time would the faster train require to overtake the slower train?
Total distance to be covered = 140 + 160 m = 300 m
Relative speed = 50 – 40 = 10 km / hr = 10 x (5 / 18) m / sec = 50 / 18 m / sec
Therefore, the time is taken by the faster train to overtake the slower train = 300 / (50/18) = 108 sec
Q6: A 500 m long train takes 36 seconds to cross a man walking in the opposite direction at the speed of 10 km/hr. Find the speed of the train.
Let the speed of the train be T km/hr.
=> Relative speed = T + 10 km / hr
=> Length of the train = 500 m = 0.5 km
We know that Distance = Speed x Time
=> 0.5 = (T + 10) x (36 / 3600)
=> 50 = T + 10
=> T = 40 km/hr
Therefore, the speed of the train is 40 km/hr.
Q7: A non-stop train started from Delhi towards Mumbai and at the same time, another non-stop train started from Mumbai towards Delhi. If after meeting in Bhopal they took 9 and 16 hours respectively to reach their destinations, find the speed of the train that started from Delhi, given that the speed of the train that started from Mumbai was moving at a speed of 90 km/hr.
We know that for two trains starting at the same time, S1: S2 = T21/2: T11/2
Here, S2 = 90 km/hr
T1 = 9 hrs
T2 = 16 hrs
=> S1 : 90 = 4 : 3
=> S1 = 120 km/hr
Therefore, the speed of the train that started from Delhi = 120 km/hr
Q8: A boatman can row a boat upstream at 14 km/hr and downstream at 20 km/hr. Find the speed of the boat in still water and the speed of the stream.
We are given that speed downstream, D = 20 km / hr and speed upstream, U = 14 km / hr
Therefore, Speed of boat in still water = 0.5 x (D + U) km / hr = 0.5 x (14 + 20) = 17 km / hr
Also, speed of the stream = 0.5 x (D – U) km / hr = 0.5 x (20 – 14) = 3 km / hr
Another method :
Speed of the stream = 0.5 x (D – U) = 0.5 x 6 = 3 km / hr
Speed of the boat in still water = Speed of the stream + Speed Upstream = 3 + 14 = 17 km / hr
Q9: A boatman can row a boat at the speed of 5 km upstream and 15 km downstream. To cover upstream he needs 2.5 hours and to cover downstream, he needs 10 hours. Find the speed of the stream and the speed of the boat in still water.
We are given that the boatman covers 5 km upstream in 2.5 hours and 15 km downstream in 10 hours.
=> Speed upstream, U = 5 / 2.5 = 2 km / hr
=> Speed downstream, D = 15 / 1.5 = 10 km / hr
Therefore, Speed of boat in still water = 0.5 x (D + U) km / hr = 0.5 x (10 + 2) = 6 km / hr
Also, speed of the stream = 0.5 x (D – U) km / hr = 0.5 x (10 – 2) = 4 km / hr
Q10: A man has to go from a port to an island and return. He can row a boat with a speed of 7 km/hr in still water. The speed of the stream is 2 km/hr. If he takes 56 minutes to complete the round trip, find the distance between the port and the island.
Speed upstream = 7 – 2 = 5 km / hr
Speed downstream = 7 + 2 = 9 km / hr
Let the distance between the port and the island be D km. Also, we know that Time = Distance / Speed
=> (D/5) + (D/9) = 56/60
=> (14 D) / 45 = 56 / 60
=> D = 3 km
Therefore, the distance between the port and the island = 3 km
Q11: In a boat race, a person rows a boat 6 km upstream and returns to the starting point in 4 hours. If the speed of the stream is 2 km/hr, find the speed of the boat in still water.
Let the speed of the boat in still water be B km/hr.
=> Speed upstream = (B – 2) km/hr
=> Speed downstream = (B + 2) km / hr
We know that Time = Distance / Speed
=> 6/(B-2) + 6/(B+2) = 4
=> 6 B + 12 + 6 B – 12 = 4 (B – 2) (B + 2)
=> 12 B = 4 (B – 2) (B + 2)
=> 3 B = B2 – 4
=> B2 – 3 B – 4 = 0
=> (B + 1) (B – 4) = 0
=> B = 4 km/hr (Speed cannot be negative)
Q12: A racer can row a boat 30 km upstream and 44 km downstream in 10 hours. Also, he can row 40 km upstream and 55 km downstream in 13 hours. Find the speed of the boat in still water and the speed of the stream.
Let the speed upstream be U km/hr and the speed downstream be D km/hr.
We know that Distance / Speed = Time
=> (30 / U) + (44 / D) = 10 and (40 / U) + (55 / D) = 13
Solving the above pair of linear equations, we get
D = 11 km/hr
U = 5 km/hr
Therefore, Speed of boat in still water = 0.5 x (D + U) km / hr = 0.5 x (11 + 5) = 8 km / hr
Also, speed of the stream = 0.5 x (D – U) km / hr = 0.5 x (11 – 5) = 3 km / hr
Problem on Trains, Boat and streams | Set-2
Test your knowledge of Boats and Streams in Quantitative Aptitude with the quiz linked below, containing numerous practice questions to help you master the topic:-
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