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Kanai and Balai ran around a circular path with constant speeds. They started from the same place and at the same time in opposite directions. After their first meeting, Balai took 1 minute to go back to starting place. If Kanai and Balai need 6 minutes and 't' minutes respectively to complete one round of the path, find the possible value of t.
- a)2
- b)3
- c)4
- d)5
Correct answer is option 'B'. Can you explain this answer?
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Kanai and Balai ran around a circular path with constant speeds. They...
Given information:
- Kanai and Balai run around a circular path with constant speeds.
- They started from the same place and at the same time in opposite directions.
- After their first meeting, Balai took 1 minute to go back to the starting place.
- Kanai and Balai need 6 minutes and 't' minutes respectively to complete one round of the path.
To find: The possible value of 't'.
Approach:
To find the value of 't', we need to analyze the time taken by Kanai and Balai to meet again after their first meeting.
1. Meeting point after the first round:
- Let's assume that Balai's speed is 'b' units per minute and Kanai's speed is 'k' units per minute.
- Since they started in opposite directions, their relative speed is the sum of their speeds, i.e., (b + k) units per minute.
- The time taken to meet after the first round is the distance traveled by Balai divided by the relative speed, which is 1 minute.
- Therefore, the distance covered by Balai in 1 minute is (b + k) units.
2. Time taken by Balai to complete one round:
- The time taken by Balai to complete one round is the time taken to meet after the first round plus the time taken to return to the starting point.
- Since Balai took 1 minute to return to the starting place, the total time taken by Balai to complete one round is (1 + 1) minute.
3. Time taken by Kanai to complete one round:
- The time taken by Kanai to complete one round is 6 minutes.
4. Ratio of the speeds:
- The ratio of the speeds of Balai and Kanai can be determined by the ratio of the distances traveled by them in the same time.
- The distance traveled by Balai in 1 minute is (b + k) units, and the distance traveled by Kanai in 1 minute is k units.
- Therefore, the ratio of their speeds is (b + k) : k.
5. Finding the value of 't':
- Since Balai takes 2 minutes to complete one round, the distance traveled by Balai in 2 minutes is 2(b + k) units.
- Since Kanai takes 6 minutes to complete one round, the distance traveled by Kanai in 6 minutes is 6k units.
- The ratio of the distances traveled by Balai and Kanai in the same time is equal to the ratio of their speeds.
- Therefore, we have the equation: 2(b + k) : 6k = (b + k) : k.
- Simplifying this equation, we get: 2(b + k) = 6k.
- Dividing both sides of the equation by 2, we get: b + k = 3k.
- Subtracting k from both sides of the equation, we get: b = 2k.
- This implies that the ratio of their speeds is 2 : 1.
Hence, the possible value of 't' is 3, which corresponds to option B.
- Kanai and Balai run around a circular path with constant speeds.
- They started from the same place and at the same time in opposite directions.
- After their first meeting, Balai took 1 minute to go back to the starting place.
- Kanai and Balai need 6 minutes and 't' minutes respectively to complete one round of the path.
To find: The possible value of 't'.
Approach:
To find the value of 't', we need to analyze the time taken by Kanai and Balai to meet again after their first meeting.
1. Meeting point after the first round:
- Let's assume that Balai's speed is 'b' units per minute and Kanai's speed is 'k' units per minute.
- Since they started in opposite directions, their relative speed is the sum of their speeds, i.e., (b + k) units per minute.
- The time taken to meet after the first round is the distance traveled by Balai divided by the relative speed, which is 1 minute.
- Therefore, the distance covered by Balai in 1 minute is (b + k) units.
2. Time taken by Balai to complete one round:
- The time taken by Balai to complete one round is the time taken to meet after the first round plus the time taken to return to the starting point.
- Since Balai took 1 minute to return to the starting place, the total time taken by Balai to complete one round is (1 + 1) minute.
3. Time taken by Kanai to complete one round:
- The time taken by Kanai to complete one round is 6 minutes.
4. Ratio of the speeds:
- The ratio of the speeds of Balai and Kanai can be determined by the ratio of the distances traveled by them in the same time.
- The distance traveled by Balai in 1 minute is (b + k) units, and the distance traveled by Kanai in 1 minute is k units.
- Therefore, the ratio of their speeds is (b + k) : k.
5. Finding the value of 't':
- Since Balai takes 2 minutes to complete one round, the distance traveled by Balai in 2 minutes is 2(b + k) units.
- Since Kanai takes 6 minutes to complete one round, the distance traveled by Kanai in 6 minutes is 6k units.
- The ratio of the distances traveled by Balai and Kanai in the same time is equal to the ratio of their speeds.
- Therefore, we have the equation: 2(b + k) : 6k = (b + k) : k.
- Simplifying this equation, we get: 2(b + k) = 6k.
- Dividing both sides of the equation by 2, we get: b + k = 3k.
- Subtracting k from both sides of the equation, we get: b = 2k.
- This implies that the ratio of their speeds is 2 : 1.
Hence, the possible value of 't' is 3, which corresponds to option B.
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Community Answer
Kanai and Balai ran around a circular path with constant speeds. They...
Let x and y be the distances travelled by Kanai and Balai in T minutes respectively till first meeting.
Let the speed of Kanai and Balai be Ks and Bs respectively
Therefore, x = Ks T and y = BsT è(y/x) = (Bs/Ks)
After first meeting, distance travelled by Kanai is y in 6-T minutes
6-T = (y/Ks) and T = x/Ks
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Kanai and Balai ran around a circular path with constant speeds. They started from the same place and at the same time in opposite directions. After their first meeting, Balai took 1 minute to go back to starting place. If Kanai and Balai need 6 minutes and 't' minutes respectively to complete one round of the path, find the possible value of t.a)2b)3c)4d)5Correct answer is option 'B'. Can you explain this answer?
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Kanai and Balai ran around a circular path with constant speeds. They started from the same place and at the same time in opposite directions. After their first meeting, Balai took 1 minute to go back to starting place. If Kanai and Balai need 6 minutes and 't' minutes respectively to complete one round of the path, find the possible value of t.a)2b)3c)4d)5Correct 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 Kanai and Balai ran around a circular path with constant speeds. They started from the same place and at the same time in opposite directions. After their first meeting, Balai took 1 minute to go back to starting place. If Kanai and Balai need 6 minutes and 't' minutes respectively to complete one round of the path, find the possible value of t.a)2b)3c)4d)5Correct 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 Kanai and Balai ran around a circular path with constant speeds. They started from the same place and at the same time in opposite directions. After their first meeting, Balai took 1 minute to go back to starting place. If Kanai and Balai need 6 minutes and 't' minutes respectively to complete one round of the path, find the possible value of t.a)2b)3c)4d)5Correct answer is option 'B'. Can you explain this answer?.
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