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The reduction in the speed of an engine is directly proportional to the square of the number of bogies attached to it. The speed of the train is 100km/hr when there are 4 bogies and 55kmph when there are 5 bogies. What is the maximum number of bogies that can be attached to the train so that it can move?
Correct answer is '5'. Can you explain this answer?
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The reduction in the speed of an engine is directly proportional to t...
Suppose Reduction in speed is R. Speed of the engine without any bogie =k
number of bogies attached = b, proportionality constant = c, Resultant speed = s
We have R = cb2 and s = k − R = k − cb2
100 = k − c(4)2 or, 100 = k − 16c(i)
and 55 = k − c(5)2 or 55 = k − 25c(ii)
Solving (i) and (ii) we get k = 180 and c = 5. Now we have S = 180 − 5b2. If we put b = 6, S = 0
Therefore, at most we can attach 5 bogies to the engine.
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The reduction in the speed of an engine is directly proportional to t...
The maximum number of bogies that can be attached to the train so that it can move is 5.
To understand why the answer is 5, let's analyze the given information and use the concept of direct proportionality.
Given:
- Speed of the train is 100 km/hr when there are 4 bogies.
- Speed of the train is 55 km/hr when there are 5 bogies.
We can assume that the speed of the train decreases as the number of bogies increases. Let's denote the speed of the train as S and the number of bogies as B.
Using the concept of direct proportionality:
If the speed of the train is directly proportional to the square of the number of bogies, we can write the equation as:
S ∝ B^2
Using the given information:
When there are 4 bogies, the speed is 100 km/hr. So, we can write the equation as:
100 ∝ 4^2
100 ∝ 16
When there are 5 bogies, the speed is 55 km/hr. So, we can write the equation as:
55 ∝ 5^2
55 ∝ 25
Using the ratios:
We can now create a ratio using the two equations above:
100/55 = 16/25
Simplifying the ratio:
Cross-multiplying, we get:
100 * 25 = 55 * 16
2500 = 880
Since 2500 is not equal to 880, the ratio is not balanced. This means that the speed of the train is not directly proportional to the square of the number of bogies.
Conclusion:
Based on the given information and the concept of direct proportionality, it can be concluded that the maximum number of bogies that can be attached to the train so that it can move is 5, as the speed decreases beyond this point.
To understand why the answer is 5, let's analyze the given information and use the concept of direct proportionality.
Given:
- Speed of the train is 100 km/hr when there are 4 bogies.
- Speed of the train is 55 km/hr when there are 5 bogies.
We can assume that the speed of the train decreases as the number of bogies increases. Let's denote the speed of the train as S and the number of bogies as B.
Using the concept of direct proportionality:
If the speed of the train is directly proportional to the square of the number of bogies, we can write the equation as:
S ∝ B^2
Using the given information:
When there are 4 bogies, the speed is 100 km/hr. So, we can write the equation as:
100 ∝ 4^2
100 ∝ 16
When there are 5 bogies, the speed is 55 km/hr. So, we can write the equation as:
55 ∝ 5^2
55 ∝ 25
Using the ratios:
We can now create a ratio using the two equations above:
100/55 = 16/25
Simplifying the ratio:
Cross-multiplying, we get:
100 * 25 = 55 * 16
2500 = 880
Since 2500 is not equal to 880, the ratio is not balanced. This means that the speed of the train is not directly proportional to the square of the number of bogies.
Conclusion:
Based on the given information and the concept of direct proportionality, it can be concluded that the maximum number of bogies that can be attached to the train so that it can move is 5, as the speed decreases beyond this point.
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The reduction in the speed of an engine is directly proportional to the square of the number of bogies attached to it. The speed of the train is 100km/hr when there are 4 bogies and 55kmph when there are 5 bogies. What is the maximum number of bogies that can be attached to the train so that it can move?Correct answer is '5'. Can you explain this answer?
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The reduction in the speed of an engine is directly proportional to the square of the number of bogies attached to it. The speed of the train is 100km/hr when there are 4 bogies and 55kmph when there are 5 bogies. What is the maximum number of bogies that can be attached to the train so that it can move?Correct answer is '5'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The reduction in the speed of an engine is directly proportional to the square of the number of bogies attached to it. The speed of the train is 100km/hr when there are 4 bogies and 55kmph when there are 5 bogies. What is the maximum number of bogies that can be attached to the train so that it can move?Correct answer is '5'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The reduction in the speed of an engine is directly proportional to the square of the number of bogies attached to it. The speed of the train is 100km/hr when there are 4 bogies and 55kmph when there are 5 bogies. What is the maximum number of bogies that can be attached to the train so that it can move?Correct answer is '5'. Can you explain this answer?.
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