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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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DIRECTIONS for the question:Solve the following question and mark the ...
**Given information:**
- 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.

To find:
- The stream speed and the increase in the speed of the boat.

**Assumptions:**
- The river has a uniform flow throughout.
- The time taken by both boats to reach their respective destinations is the same.
- The distance between points A and B is D km.

**Solution:**

Let the speed of the stream be S kmph.

**Meeting point:**
- Let's assume the point where the two boats meet is M.
- Let the distance between point A and point M be x km.
- Therefore, the distance between point B and point M will be (D - x) km.

**Time taken by each boat to reach the meeting point:**
- Boat 1: The time taken by boat 1 to reach the meeting point is x / (5 + S) hours.
- Boat 2: The time taken by boat 2 to reach the meeting point is (D - x) / (5 - S) hours.

**Distance covered by each boat to reach the meeting point:**
- Boat 1: The distance covered by boat 1 to reach the meeting point is x km.
- Boat 2: The distance covered by boat 2 to reach the meeting point is (D - x) km.

**Given condition:**
- The first boat covers half the distance covered by the second boat when they meet.
- This means x = (D - x) / 2.

Solving the above equation, we get:
2x = D - x
3x = D
x = D/3

**Time taken by each boat to reach their respective destinations after meeting point:**
- Boat 1: The time taken by boat 1 to reach its destination is (D - x) / (5 + V) hours. (where V is the increased speed of boat 1)
- Boat 2: The time taken by boat 2 to reach its destination is x / (5 - S) hours.

**Given condition:**
- Both the boats reach their respective destinations at the same time.
- This implies that the time taken by boat 1 to reach its destination is equal to the time taken by boat 2 to reach its destination.

Therefore, we can equate the two time expressions and solve for V.

((D - x) / (5 + V)) = (x / (5 - S))

Simplifying the equation:

((D - x) / (5 + V)) = (x / (5 - S))

Cross-multiplying:

(D - x)(5 - S) = x(5 + V)

Expanding and simplifying:

5D - Dx - 5S + Sx = 5x + Vx

Rearranging:

5D - 5S = Vx + Dx + 5x - Sx

Combining like terms:

5D - 5S = (V + D - S)x

Dividing both sides by (V + D - S):

(5D - 5S)/(V + D -
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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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