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A cyclist starts from point A at 9 am and heads towards point B, which is 100 km away. A car starts from point A at 10 am and heads towards point B at a speed of 25 km/hr. The car overtakes the cyclist at 10:40 am. A motorist starts from point B at 11 am and crosses the cyclist at 1 pm. At what distance from the point A does the motorist and cyclist cross each other.
- a)30 km
- b)35 km
- c)40 km
- d)45 km
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A cyclist starts from point A at 9 am and heads towards point B, which...
In 40 minutes (i.e. 40/60 hr), the car has travelled 25 x (40/60) = 100/6 km. i.e., the cyclist travells 100/6 km in (1 hr 40 minutes = ) 100 minutes
We need to find the distance between A and the point where the cyclist and the motorist crosses each other.
At this moment, the cyclist has travelled for 4 hours i.e., 240 minutes from A.
We need to find the distance between A and the point where the cyclist and the motorist crosses each other.
At this moment, the cyclist has travelled for 4 hours i.e., 240 minutes from A.
i.e., the distance covered by the cyclist = (100/6) * 240/100 = 40 km.
Hence, option 3.
Hence, option 3.
Most Upvoted Answer
A cyclist starts from point A at 9 am and heads towards point B, which...
Problem Analysis:
We need to find the distance from point A where the motorist and the cyclist cross each other. We are given the following information:
- The distance between A and B is 100 km.
- Cyclist starts from point A at 9 am.
- Car starts from point A at 10 am and overtakes the cyclist at 10:40 am.
- Motorist starts from point B at 11 am and crosses the cyclist at 1 pm.
We can use the information given to calculate the speed and distance of the cyclist and the car.
Solution:
Let's first calculate the speed of the cyclist:
- The cyclist starts at 9 am and is overtaken by the car at 10:40 am.
- So, the cyclist rides for 1 hour and 40 minutes (10:40 am - 9 am = 1 hour 40 minutes).
- Let's assume the speed of the cyclist is x km/hr.
- Distance covered by the cyclist in 1 hour 40 minutes = (x * 100) / 60 km (distance = speed x time)
- This distance is equal to the distance covered by the car when it overtakes the cyclist.
- Distance covered by the car in 40 minutes (10:40 am - 10 am = 40 minutes) = 25 * (40/60) = 16.67 km (distance = speed x time)
- Equating the two distances, we get:
(x * 100) / 60 = 16.67
x = 10 km/hr
Now, let's calculate the distance between the car and the cyclist when the car overtakes the cyclist:
- The speed of the car is 25 km/hr and it overtakes the cyclist.
- Let's assume the distance between the car and the cyclist at the time of overtaking is d km.
- Time taken by the car to cover this distance = 40 minutes = 2/3 hour.
- Time taken by the cyclist to cover this distance = d/10 hours.
- Equating the two times, we get:
d/10 = 2/3
d = 6.67 km
The distance between the car and the cyclist at the time of overtaking is 6.67 km.
Now, let's calculate the distance covered by the cyclist from 9 am to 1 pm:
- The cyclist rides for 4 hours (9 am to 1 pm).
- Let's assume the distance covered by the cyclist in 4 hours is D km.
- Distance covered by the cyclist in 1 hour = 10 km (speed of the cyclist).
- Distance covered by the cyclist in 4 hours = 10 * 4 = 40 km.
We know that the motorist crosses the cyclist at 1 pm. At this time, the cyclist has covered 40 km. So, the distance between the motorist and the cyclist is 100 - 40 = 60 km.
Now, we need to find the distance from point A where the motorist and cyclist cross each other. Let's assume this distance is x km from point A.
- The time taken by the motorist to cover the distance x km from point B = x/25 hours (speed of the motorist is 25 km/hr).
- The time taken by the cyclist to cover the distance (100 - x) km from point A = (100
We need to find the distance from point A where the motorist and the cyclist cross each other. We are given the following information:
- The distance between A and B is 100 km.
- Cyclist starts from point A at 9 am.
- Car starts from point A at 10 am and overtakes the cyclist at 10:40 am.
- Motorist starts from point B at 11 am and crosses the cyclist at 1 pm.
We can use the information given to calculate the speed and distance of the cyclist and the car.
Solution:
Let's first calculate the speed of the cyclist:
- The cyclist starts at 9 am and is overtaken by the car at 10:40 am.
- So, the cyclist rides for 1 hour and 40 minutes (10:40 am - 9 am = 1 hour 40 minutes).
- Let's assume the speed of the cyclist is x km/hr.
- Distance covered by the cyclist in 1 hour 40 minutes = (x * 100) / 60 km (distance = speed x time)
- This distance is equal to the distance covered by the car when it overtakes the cyclist.
- Distance covered by the car in 40 minutes (10:40 am - 10 am = 40 minutes) = 25 * (40/60) = 16.67 km (distance = speed x time)
- Equating the two distances, we get:
(x * 100) / 60 = 16.67
x = 10 km/hr
Now, let's calculate the distance between the car and the cyclist when the car overtakes the cyclist:
- The speed of the car is 25 km/hr and it overtakes the cyclist.
- Let's assume the distance between the car and the cyclist at the time of overtaking is d km.
- Time taken by the car to cover this distance = 40 minutes = 2/3 hour.
- Time taken by the cyclist to cover this distance = d/10 hours.
- Equating the two times, we get:
d/10 = 2/3
d = 6.67 km
The distance between the car and the cyclist at the time of overtaking is 6.67 km.
Now, let's calculate the distance covered by the cyclist from 9 am to 1 pm:
- The cyclist rides for 4 hours (9 am to 1 pm).
- Let's assume the distance covered by the cyclist in 4 hours is D km.
- Distance covered by the cyclist in 1 hour = 10 km (speed of the cyclist).
- Distance covered by the cyclist in 4 hours = 10 * 4 = 40 km.
We know that the motorist crosses the cyclist at 1 pm. At this time, the cyclist has covered 40 km. So, the distance between the motorist and the cyclist is 100 - 40 = 60 km.
Now, we need to find the distance from point A where the motorist and cyclist cross each other. Let's assume this distance is x km from point A.
- The time taken by the motorist to cover the distance x km from point B = x/25 hours (speed of the motorist is 25 km/hr).
- The time taken by the cyclist to cover the distance (100 - x) km from point A = (100
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A cyclist starts from point A at 9 am and heads towards point B, which is 100 km away. A car starts from point A at 10 am and heads towards point B at a speed of 25 km/hr. The car overtakes the cyclist at 10:40 am. A motorist starts from point B at 11 am and crosses the cyclist at 1 pm. At what distance from the point A does the motorist and cyclist cross each other.a)30 kmb)35 kmc)40 kmd)45 kmCorrect answer is option 'C'. Can you explain this answer?
Question Description
A cyclist starts from point A at 9 am and heads towards point B, which is 100 km away. A car starts from point A at 10 am and heads towards point B at a speed of 25 km/hr. The car overtakes the cyclist at 10:40 am. A motorist starts from point B at 11 am and crosses the cyclist at 1 pm. At what distance from the point A does the motorist and cyclist cross each other.a)30 kmb)35 kmc)40 kmd)45 kmCorrect answer is option 'C'. 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 starts from point A at 9 am and heads towards point B, which is 100 km away. A car starts from point A at 10 am and heads towards point B at a speed of 25 km/hr. The car overtakes the cyclist at 10:40 am. A motorist starts from point B at 11 am and crosses the cyclist at 1 pm. At what distance from the point A does the motorist and cyclist cross each other.a)30 kmb)35 kmc)40 kmd)45 kmCorrect answer is option 'C'. 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 starts from point A at 9 am and heads towards point B, which is 100 km away. A car starts from point A at 10 am and heads towards point B at a speed of 25 km/hr. The car overtakes the cyclist at 10:40 am. A motorist starts from point B at 11 am and crosses the cyclist at 1 pm. At what distance from the point A does the motorist and cyclist cross each other.a)30 kmb)35 kmc)40 kmd)45 kmCorrect answer is option 'C'. Can you explain this answer?.
A cyclist starts from point A at 9 am and heads towards point B, which is 100 km away. A car starts from point A at 10 am and heads towards point B at a speed of 25 km/hr. The car overtakes the cyclist at 10:40 am. A motorist starts from point B at 11 am and crosses the cyclist at 1 pm. At what distance from the point A does the motorist and cyclist cross each other.a)30 kmb)35 kmc)40 kmd)45 kmCorrect answer is option 'C'. 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 starts from point A at 9 am and heads towards point B, which is 100 km away. A car starts from point A at 10 am and heads towards point B at a speed of 25 km/hr. The car overtakes the cyclist at 10:40 am. A motorist starts from point B at 11 am and crosses the cyclist at 1 pm. At what distance from the point A does the motorist and cyclist cross each other.a)30 kmb)35 kmc)40 kmd)45 kmCorrect answer is option 'C'. 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 starts from point A at 9 am and heads towards point B, which is 100 km away. A car starts from point A at 10 am and heads towards point B at a speed of 25 km/hr. The car overtakes the cyclist at 10:40 am. A motorist starts from point B at 11 am and crosses the cyclist at 1 pm. At what distance from the point A does the motorist and cyclist cross each other.a)30 kmb)35 kmc)40 kmd)45 kmCorrect answer is option 'C'. Can you explain this answer?.
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ample number of questions to practice A cyclist starts from point A at 9 am and heads towards point B, which is 100 km away. A car starts from point A at 10 am and heads towards point B at a speed of 25 km/hr. The car overtakes the cyclist at 10:40 am. A motorist starts from point B at 11 am and crosses the cyclist at 1 pm. At what distance from the point A does the motorist and cyclist cross each other.a)30 kmb)35 kmc)40 kmd)45 kmCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice CAT tests.
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