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DIRECTIONS for the question:
Solve the following question and mark the best possible option.
Two boats start from points A and B of a river and travel towards each other with the same speeds of 5 kmph. The first boat covers half the distance covered by the second boat when they meet. After that point the first boat increases its speed and both the boats reach their respective destinations at the same time. What was the stream speed and the increase in the speed of the boat?
  • a)
    5/3 kmph, 10 kmph
  • b)
    5 kmph, 10 kmph
  • c)
    5/3 kmph, 11 kmph
  • d)
    10/3 kmph, 5 kmph
Correct answer is option 'A'. Can you explain this answer?
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DIRECTIONS for the question: Solve the following question and mark the...
Let the initial distance between the point A and B be 3x km, the stream speed be s kmph and the increase in speed of the first boat be y kmph.
Since the speed of both the boats is same and the first boat covers half the distance covered by the second boat, so the first boat is moving upstream and second boat downstream.
Thus x/(5 – s) = 2x/(5 + s)
5x + sx = 10x – 2sx
3sx = 5x
s = 5/3 kmph.
After meeting, the first boat increases its speed and both reach their respective destinations at the same time, hence,
2x/(5 + y – 5/3) = x/(5 + 5/3)
So, y = 10 kmph.
Hence option 1.
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Question Analysis:
We are given that two boats start from points A and B of a river and travel towards each other with the same speeds of 5 kmph. The first boat covers half the distance covered by the second boat when they meet. After that point, the first boat increases its speed and both boats reach their respective destinations at the same time. We need to find the stream speed and the increase in the speed of the boat.

Let's assume:
Let the distance between point A and point B be 'd' km.
Let the time taken by both boats to meet be 't' hours.
Let the stream speed be 'x' kmph.
Let the increase in the speed of the first boat be 'y' kmph.

Boat Speed:
Since both boats travel towards each other with the same speeds of 5 kmph, the speed of each boat with respect to the river is 5 kmph.

Distance Covered:
- The first boat covers half the distance covered by the second boat when they meet. Therefore, the distance covered by the first boat is (1/2)d km and the distance covered by the second boat is (1)d km.
- After they meet, both boats cover the remaining distance at the same time. Therefore, the distance covered by each boat after they meet is (1/2)d km.

Time and Speed Relationship:
- Time = Distance / Speed

Time Taken by the First Boat:
- Time taken by the first boat to meet the second boat = (1/2)d / (5+x) hours (as the speed of the first boat increases later)
- Time taken by the first boat to cover the remaining distance = (1/2)d / (5+y) hours

Time Taken by the Second Boat:
- Time taken by the second boat to meet the first boat = (1)d / (5-x) hours (as the speed of the first boat increases later)
- Time taken by the second boat to cover the remaining distance = (1/2)d / (5+y) hours

Equating the Times:
Since both boats reach their respective destinations at the same time, we can equate the times taken by both boats.

(1/2)d / (5+x) + (1/2)d / (5+y) = (1)d / (5-x) + (1/2)d / (5+y)

Simplifying the Equation:
To simplify the equation, we can multiply both sides by the least common multiple of the denominators, which is (5+x)(5-x)(5+y).

(5+y)d + (5+x)d = (5-x)d + (5+y)(1/2)d

Simplifying further, we get:

(5+y)(5-x) = 2(5-x)(5+y)

Solving for x and y:
Expanding both sides of the equation, we get:

25 + 5y - 5x - xy = 50 - 2x - 2y

Rearranging the terms, we get:

3x + 7y = 25

This is a linear equation in two variables. To solve for x and y, we need one more equation.

Using the Distance:
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DIRECTIONS for the question: Solve the following question and mark the best possible option.Two boats start from points A and B of a river and travel towards each other with the same speeds of 5 kmph. The first boat covers half the distance covered by the second boat when they meet. After that point the first boat increases its speed and both the boats reach their respective destinations at the same time. What was the stream speed and the increase in the speed of the boat?a)5/3 kmph, 10 kmphb)5 kmph, 10 kmphc)5/3 kmph, 11 kmphd)10/3 kmph, 5 kmphCorrect answer is option 'A'. Can you explain this answer?
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DIRECTIONS for the question: Solve the following question and mark the best possible option.Two boats start from points A and B of a river and travel towards each other with the same speeds of 5 kmph. The first boat covers half the distance covered by the second boat when they meet. After that point the first boat increases its speed and both the boats reach their respective destinations at the same time. What was the stream speed and the increase in the speed of the boat?a)5/3 kmph, 10 kmphb)5 kmph, 10 kmphc)5/3 kmph, 11 kmphd)10/3 kmph, 5 kmphCorrect answer is option 'A'. 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 DIRECTIONS for the question: Solve the following question and mark the best possible option.Two boats start from points A and B of a river and travel towards each other with the same speeds of 5 kmph. The first boat covers half the distance covered by the second boat when they meet. After that point the first boat increases its speed and both the boats reach their respective destinations at the same time. What was the stream speed and the increase in the speed of the boat?a)5/3 kmph, 10 kmphb)5 kmph, 10 kmphc)5/3 kmph, 11 kmphd)10/3 kmph, 5 kmphCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for DIRECTIONS for the question: Solve the following question and mark the best possible option.Two boats start from points A and B of a river and travel towards each other with the same speeds of 5 kmph. The first boat covers half the distance covered by the second boat when they meet. After that point the first boat increases its speed and both the boats reach their respective destinations at the same time. What was the stream speed and the increase in the speed of the boat?a)5/3 kmph, 10 kmphb)5 kmph, 10 kmphc)5/3 kmph, 11 kmphd)10/3 kmph, 5 kmphCorrect answer is option 'A'. Can you explain this answer?.
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