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Two boats A and B are travelling in opposite directions in still water. The ratio of the distances covered by them in the same time is 3:1. If they travel in opposite directions in a stream, the distance covered by A and B (in the same time) is 1:3 respectively. What is the ratio of the speed of A and speed of the water?
- a)2/1
- b)3/2
- c)4/3
- d)5/2
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Two boats A and B are travelling in opposite directions in still water...
Two boats A and B are travelling in opposite directions in still water and covers the distance in ratio 3:1 respectively.
Let the two boats travel at 3v and 1v speed.
Let the speed of the stream is 'r'.
The boats will travel in stream water:
Distance covered by A= (3v-r) t
Distance covered by B= (v+r) t
r = 2v
The ratio of the speed of A and speed of the water = 3v/2v
= 3/2
Let the two boats travel at 3v and 1v speed.
Let the speed of the stream is 'r'.
The boats will travel in stream water:
Distance covered by A= (3v-r) t
Distance covered by B= (v+r) t
r = 2v
The ratio of the speed of A and speed of the water = 3v/2v
= 3/2
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Community Answer
Two boats A and B are travelling in opposite directions in still water...
Understanding the Problem
Two boats A and B travel in opposite directions. The key information given is:
- In still water, the ratio of distances covered by A and B in the same time is 3:1.
- In a stream, the distances covered by A and B in the same time are in the ratio 1:3.
Assigning Variables
Let:
- Speed of boat A = 3x
- Speed of boat B = x
- Speed of the stream (water) = y
Distance Ratios in Still Water
In still water:
- Distance covered by A = 3x * t
- Distance covered by B = x * t
The ratio is given as 3:1, which checks out.
Distance Ratios in the Stream
In the stream:
- Effective speed of A = (3x + y)
- Effective speed of B = (x - y)
The distances covered are in the ratio 1:3:
\[
\frac{3x + y}{x - y} = \frac{1}{3}
\]
Cross-multiplying gives:
\[
3(3x + y) = 1(x - y)
\]
Expanding:
\[
9x + 3y = x - y
\]
Rearranging:
\[
8x + 4y = 0 \implies 2y = -4x \implies y = -2x
\]
Finding the Ratio of Speeds
Since speed cannot be negative, take absolute values:
\[
y = 2x
\]
Now, we find the ratio of speed of A to speed of the water:
\[
\text{Ratio} = \frac{\text{Speed of A}}{\text{Speed of water}} = \frac{3x}{2x} = \frac{3}{2}
\]
Conclusion
The ratio of the speed of A to the speed of the water is 3:2, confirming option 'B' as the correct answer.
Two boats A and B travel in opposite directions. The key information given is:
- In still water, the ratio of distances covered by A and B in the same time is 3:1.
- In a stream, the distances covered by A and B in the same time are in the ratio 1:3.
Assigning Variables
Let:
- Speed of boat A = 3x
- Speed of boat B = x
- Speed of the stream (water) = y
Distance Ratios in Still Water
In still water:
- Distance covered by A = 3x * t
- Distance covered by B = x * t
The ratio is given as 3:1, which checks out.
Distance Ratios in the Stream
In the stream:
- Effective speed of A = (3x + y)
- Effective speed of B = (x - y)
The distances covered are in the ratio 1:3:
\[
\frac{3x + y}{x - y} = \frac{1}{3}
\]
Cross-multiplying gives:
\[
3(3x + y) = 1(x - y)
\]
Expanding:
\[
9x + 3y = x - y
\]
Rearranging:
\[
8x + 4y = 0 \implies 2y = -4x \implies y = -2x
\]
Finding the Ratio of Speeds
Since speed cannot be negative, take absolute values:
\[
y = 2x
\]
Now, we find the ratio of speed of A to speed of the water:
\[
\text{Ratio} = \frac{\text{Speed of A}}{\text{Speed of water}} = \frac{3x}{2x} = \frac{3}{2}
\]
Conclusion
The ratio of the speed of A to the speed of the water is 3:2, confirming option 'B' as the correct answer.
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Two boats A and B are travelling in opposite directions in still water. The ratio of the distances covered by them in the same time is 3:1. If they travel in opposite directions in a stream, the distance covered by A and B (in the same time) is 1:3 respectively. What is the ratio of the speed of A and speed of the water?a)2/1b)3/2c)4/3d)5/2Correct answer is option 'B'. Can you explain this answer?
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Two boats A and B are travelling in opposite directions in still water. The ratio of the distances covered by them in the same time is 3:1. If they travel in opposite directions in a stream, the distance covered by A and B (in the same time) is 1:3 respectively. What is the ratio of the speed of A and speed of the water?a)2/1b)3/2c)4/3d)5/2Correct answer is option 'B'. 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 Two boats A and B are travelling in opposite directions in still water. The ratio of the distances covered by them in the same time is 3:1. If they travel in opposite directions in a stream, the distance covered by A and B (in the same time) is 1:3 respectively. What is the ratio of the speed of A and speed of the water?a)2/1b)3/2c)4/3d)5/2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two boats A and B are travelling in opposite directions in still water. The ratio of the distances covered by them in the same time is 3:1. If they travel in opposite directions in a stream, the distance covered by A and B (in the same time) is 1:3 respectively. What is the ratio of the speed of A and speed of the water?a)2/1b)3/2c)4/3d)5/2Correct answer is option 'B'. Can you explain this answer?.
Two boats A and B are travelling in opposite directions in still water. The ratio of the distances covered by them in the same time is 3:1. If they travel in opposite directions in a stream, the distance covered by A and B (in the same time) is 1:3 respectively. What is the ratio of the speed of A and speed of the water?a)2/1b)3/2c)4/3d)5/2Correct answer is option 'B'. 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 Two boats A and B are travelling in opposite directions in still water. The ratio of the distances covered by them in the same time is 3:1. If they travel in opposite directions in a stream, the distance covered by A and B (in the same time) is 1:3 respectively. What is the ratio of the speed of A and speed of the water?a)2/1b)3/2c)4/3d)5/2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two boats A and B are travelling in opposite directions in still water. The ratio of the distances covered by them in the same time is 3:1. If they travel in opposite directions in a stream, the distance covered by A and B (in the same time) is 1:3 respectively. What is the ratio of the speed of A and speed of the water?a)2/1b)3/2c)4/3d)5/2Correct answer is option 'B'. Can you explain this answer?.
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Two boats A and B are travelling in opposite directions in still water. The ratio of the distances covered by them in the same time is 3:1. If they travel in opposite directions in a stream, the distance covered by A and B (in the same time) is 1:3 respectively. What is the ratio of the speed of A and speed of the water?a)2/1b)3/2c)4/3d)5/2Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Two boats A and B are travelling in opposite directions in still water. The ratio of the distances covered by them in the same time is 3:1. If they travel in opposite directions in a stream, the distance covered by A and B (in the same time) is 1:3 respectively. What is the ratio of the speed of A and speed of the water?a)2/1b)3/2c)4/3d)5/2Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Two boats A and B are travelling in opposite directions in still water. The ratio of the distances covered by them in the same time is 3:1. If they travel in opposite directions in a stream, the distance covered by A and B (in the same time) is 1:3 respectively. What is the ratio of the speed of A and speed of the water?a)2/1b)3/2c)4/3d)5/2Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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