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A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motor cycle leaves A and moves towards B. Forty-five such motor cycles reach B by 11 am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached B by the time the cyclist reached B?
(2019)
- a)20
- b)15
- c)23
- d)22
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:0...
Time taken by cyclist to cover the distance AB = 60 min Given, starting from 10:01 am, every minute a motor cycle leaves A and moves towards B.
Forty-five such motor cycles reach B by 11 am.
Also, the speed of all the motor cycles is same This means that the 45th motor cycle, which started at 10:45 am, reached B exactly at 11 am, Rest all reached B some time before B.
Therefore, each motor cycle takes 15 min to cover the distance AB.
Now, if the cyclist doubles his speed, then he will reach B in 30 min i.e. at 10:30 am.
So, the 15th motor cycle (started at 10:15 am from A) would be the last motor cycle that reach to point B at 10:30 am.
Hence, when the cyclist had doubled his speed, then there will be 15 motor cycles would have reached B by the time the cyclist reached B.
Forty-five such motor cycles reach B by 11 am.
Also, the speed of all the motor cycles is same This means that the 45th motor cycle, which started at 10:45 am, reached B exactly at 11 am, Rest all reached B some time before B.
Therefore, each motor cycle takes 15 min to cover the distance AB.
Now, if the cyclist doubles his speed, then he will reach B in 30 min i.e. at 10:30 am.
So, the 15th motor cycle (started at 10:15 am from A) would be the last motor cycle that reach to point B at 10:30 am.
Hence, when the cyclist had doubled his speed, then there will be 15 motor cycles would have reached B by the time the cyclist reached B.
Most Upvoted Answer
A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:0...
Problem Analysis:
Let's assume the distance between A and B is D km and the speed of the cyclist is S km/h. The cyclist takes 1 hour (from 10 am to 11 am) to cover the distance D. Therefore, D = S km/h * 1 hour.
The first motorbike leaves A at 10:01 am and reaches B in 59 minutes (from 10:01 am to 11 am). Therefore, the speed of each motorbike is D km / 59 minutes.
Now, let's consider the scenario where the cyclist doubles his speed. His new speed is 2S km/h. The cyclist now takes 30 minutes (half the time) to cover the distance D. Therefore, D = 2S km/h * 0.5 hour.
Solution:
To find out how many motorbikes would reach B by the time the cyclist reaches B, we need to calculate the time it takes for each motorbike to reach B and compare it with the time taken by the cyclist.
Let's assume that x motorbikes reach B by the time the cyclist reaches B. The time taken for the first motorbike to reach B is 59 minutes, the second motorbike takes 58 minutes, the third motorbike takes 57 minutes, and so on.
Therefore, the sum of the times taken by the x motorbikes is given by:
59 + 58 + 57 + ... + (59 - x + 1) = x(59 + (59 - x + 1))/2 = x(119 - x)/2
Since the cyclist takes 30 minutes to cover the distance D, we can set up the equation:
D = 2S km/h * 0.5 hour
D = S km/h * 1 hour
2S * 0.5 = S
S = D/2
Now, substituting the value of S in terms of D in the equation for the sum of the times taken by the motorbikes:
x(119 - x)/2 = D/2
Simplifying the equation:
x(119 - x) = D
Since D = S km/h * 1 hour = D/2 km/h * 0.5 hour, we can rewrite the equation as:
x(119 - x) = x(119 - x)
Therefore, the number of motorbikes that would reach B by the time the cyclist reaches B is equal to the number of motorbikes that would reach B by the time the cyclist reaches B.
Substituting the given values, we have:
45(119 - 45) = x(119 - x)
45 * 74 = x(119 - x)
3330 = x(119 - x)
Now, we need to solve the equation for x.
Let's assume the distance between A and B is D km and the speed of the cyclist is S km/h. The cyclist takes 1 hour (from 10 am to 11 am) to cover the distance D. Therefore, D = S km/h * 1 hour.
The first motorbike leaves A at 10:01 am and reaches B in 59 minutes (from 10:01 am to 11 am). Therefore, the speed of each motorbike is D km / 59 minutes.
Now, let's consider the scenario where the cyclist doubles his speed. His new speed is 2S km/h. The cyclist now takes 30 minutes (half the time) to cover the distance D. Therefore, D = 2S km/h * 0.5 hour.
Solution:
To find out how many motorbikes would reach B by the time the cyclist reaches B, we need to calculate the time it takes for each motorbike to reach B and compare it with the time taken by the cyclist.
Let's assume that x motorbikes reach B by the time the cyclist reaches B. The time taken for the first motorbike to reach B is 59 minutes, the second motorbike takes 58 minutes, the third motorbike takes 57 minutes, and so on.
Therefore, the sum of the times taken by the x motorbikes is given by:
59 + 58 + 57 + ... + (59 - x + 1) = x(59 + (59 - x + 1))/2 = x(119 - x)/2
Since the cyclist takes 30 minutes to cover the distance D, we can set up the equation:
D = 2S km/h * 0.5 hour
D = S km/h * 1 hour
2S * 0.5 = S
S = D/2
Now, substituting the value of S in terms of D in the equation for the sum of the times taken by the motorbikes:
x(119 - x)/2 = D/2
Simplifying the equation:
x(119 - x) = D
Since D = S km/h * 1 hour = D/2 km/h * 0.5 hour, we can rewrite the equation as:
x(119 - x) = x(119 - x)
Therefore, the number of motorbikes that would reach B by the time the cyclist reaches B is equal to the number of motorbikes that would reach B by the time the cyclist reaches B.
Substituting the given values, we have:
45(119 - 45) = x(119 - x)
45 * 74 = x(119 - x)
3330 = x(119 - x)
Now, we need to solve the equation for x.
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A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motor cycle leaves A and moves towards B. Forty-five such motor cycles reach B by 11 am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached B by the time the cyclist reached B?(2019)a)20b)15c)23d)22Correct answer is option 'B'. Can you explain this answer?
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A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motor cycle leaves A and moves towards B. Forty-five such motor cycles reach B by 11 am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached B by the time the cyclist reached B?(2019)a)20b)15c)23d)22Correct 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 A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motor cycle leaves A and moves towards B. Forty-five such motor cycles reach B by 11 am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached B by the time the cyclist reached B?(2019)a)20b)15c)23d)22Correct 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 A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motor cycle leaves A and moves towards B. Forty-five such motor cycles reach B by 11 am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached B by the time the cyclist reached B?(2019)a)20b)15c)23d)22Correct answer is option 'B'. Can you explain this answer?.
A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motor cycle leaves A and moves towards B. Forty-five such motor cycles reach B by 11 am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached B by the time the cyclist reached B?(2019)a)20b)15c)23d)22Correct 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 A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motor cycle leaves A and moves towards B. Forty-five such motor cycles reach B by 11 am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached B by the time the cyclist reached B?(2019)a)20b)15c)23d)22Correct 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 A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motor cycle leaves A and moves towards B. Forty-five such motor cycles reach B by 11 am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached B by the time the cyclist reached B?(2019)a)20b)15c)23d)22Correct answer is option 'B'. Can you explain this answer?.
Solutions for A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motor cycle leaves A and moves towards B. Forty-five such motor cycles reach B by 11 am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached B by the time the cyclist reached B?(2019)a)20b)15c)23d)22Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motor cycle leaves A and moves towards B. Forty-five such motor cycles reach B by 11 am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached B by the time the cyclist reached B?(2019)a)20b)15c)23d)22Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motor cycle leaves A and moves towards B. Forty-five such motor cycles reach B by 11 am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached B by the time the cyclist reached B?(2019)a)20b)15c)23d)22Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A cyclist leaves A at 10 am and reaches B at 11 am. Starting from 10:01 am, every minute a motor cycle leaves A and moves towards B. Forty-five such motor cycles reach B by 11 am. All motor cycles have the same speed. If the cyclist had doubled his speed, how many motor cycles would have reached B by the time the cyclist reached B?(2019)a)20b)15c)23d)22Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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