Understanding the concept of "Boats and Streams" is crucial for students preparing for various exams. This topic not only enhances your problem-solving skills but also helps in scoring better in mathematics. Practicing MCQs and objective questions related to Boats and Streams allows you to grasp the essential concepts and apply them effectively in your exams. With the right practice questions, you can tackle important questions with confidence.
What You Will Practise Here
Basic definitions of speed, distance, and time in the context of boats and streams.
Formulas for calculating upstream and downstream speeds.
Concept of relative speed in moving objects.
Application of boats and streams problems in real-life scenarios.
Diagrams illustrating the movement of boats in still water and flowing streams.
Common types of problems and their solutions.
Practice questions with detailed answers for better understanding.
Exam Relevance
The topic of Boats and Streams is frequently included in the syllabus of CBSE, State Boards, NEET, and JEE. Students can expect questions that test their understanding of speed, distance, and time relationships. Common question patterns include calculating the time taken for a boat to travel a certain distance upstream or downstream, as well as problems involving the speed of the stream. Mastering this topic can significantly improve your performance in competitive exams.
Common Mistakes Students Make
Confusing upstream and downstream speeds, leading to incorrect calculations.
Neglecting to account for the speed of the stream when solving problems.
Misunderstanding the concept of relative speed in different scenarios.
Overlooking the units of measurement, which can result in errors.
Failing to draw diagrams, which can help visualize the problem better.
FAQs
Question: What is the formula for calculating the speed of a boat in still water? Answer: The speed of the boat in still water can be calculated using the formula: Speed of Boat = (Speed Downstream + Speed Upstream) / 2.
Question: How do I determine the time taken for a boat to travel a certain distance upstream? Answer: Time taken can be calculated using the formula: Time = Distance / (Speed of Boat - Speed of Stream).
Now is the time to enhance your understanding of Boats and Streams! Dive into our practice MCQs and test your knowledge to excel in your exams. Remember, consistent practice is the key to success!
Q. A boat can cover a distance of 48 km downstream in 3 hours. If the speed of the stream is 4 km/h, what is the speed of the boat in still water?
A.
12 km/h
B.
16 km/h
C.
20 km/h
D.
24 km/h
Solution
Speed downstream = 48/3 = 16 km/h. Speed of the boat in still water = speed downstream - speed of stream = 16 - 4 = 12 km/h.
Q. A boat can go 15 km upstream and 21 km downstream in 3 hours. If the speed of the stream is 3 km/h, what is the speed of the boat in still water?
A.
6 km/h
B.
9 km/h
C.
12 km/h
D.
15 km/h
Solution
Let the speed of the boat in still water be x km/h. The speed upstream = (x - 3) km/h and downstream = (x + 3) km/h. Time taken upstream = 15/(x - 3) and downstream = 21/(x + 3). Therefore, (15/(x - 3)) + (21/(x + 3)) = 3. Solving gives x = 9 km/h.
Q. A boat can go 15 km upstream and 21 km downstream in 3 hours. If the speed of the boat in still water is 10 km/h, what is the speed of the stream?
A.
2 km/h
B.
3 km/h
C.
4 km/h
D.
5 km/h
Solution
Let the speed of the stream be x km/h. The speed upstream = (10 - x) km/h and downstream = (10 + x) km/h. Time taken upstream = 15/(10 - x) and downstream = 21/(10 + x). Therefore, (15/(10 - x)) + (21/(10 + x)) = 3. Solving gives x = 3 km/h.
Q. A boat can go 24 km downstream in 3 hours. If the speed of the boat in still water is 10 km/h, what is the speed of the current?
A.
2 km/h
B.
4 km/h
C.
6 km/h
D.
8 km/h
Solution
Speed downstream = Distance/Time = 24 km / 3 h = 8 km/h. Speed of current = Speed downstream - Speed of boat in still water = 8 km/h - 10 km/h = -2 km/h (not possible).
Q. A boat can go 36 km downstream in 2 hours. If the speed of the current is 3 km/h, what is the speed of the boat in still water?
A.
15 km/h
B.
18 km/h
C.
21 km/h
D.
24 km/h
Solution
Speed downstream = Distance/Time = 36 km / 2 h = 18 km/h. Speed of boat in still water = Speed downstream - Speed of current = 18 km/h - 3 km/h = 15 km/h.
Q. A boat can travel 80 km downstream in 8 hours. If the speed of the current is 4 km/h, what is the speed of the boat in still water?
A.
8 km/h
B.
10 km/h
C.
12 km/h
D.
14 km/h
Solution
Speed downstream = Distance/Time = 80 km / 8 h = 10 km/h. Speed of boat in still water = Speed downstream - Speed of current = 10 km/h - 4 km/h = 6 km/h.
Q. A boat can travel at 10 km/h in still water. If it takes 2 hours to go upstream and 1 hour to return downstream, what is the speed of the current?
A.
2 km/h
B.
3 km/h
C.
4 km/h
D.
5 km/h
Solution
Let the speed of the current be x. Upstream speed = 10 - x, Downstream speed = 10 + x. Time upstream = 2 hours, Time downstream = 1 hour. Thus, 2(10 - x) = Distance and 1(10 + x) = Distance. Equating gives x = 3 km/h.
Q. A boat travels 20 km downstream in 2 hours. If the speed of the current is 2 km/h, what is the speed of the boat in still water?
A.
8 km/h
B.
10 km/h
C.
12 km/h
D.
14 km/h
Solution
Speed downstream = Distance/Time = 20 km / 2 h = 10 km/h. Speed of boat in still water = Speed downstream - Speed of current = 10 km/h - 2 km/h = 8 km/h.
