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Rakesh and Vishal are running along a circular path of circumference 84 km in opposite directions. They start from point O1 and meet for the first time at point O2. After meeting they exchange their speeds as well as their directions and continue running around the track. They repeat this process every time they meet. Initially, Rakesh has a speed of 85 km/hr and Vishal has a speed of 17 km/hr. What is the distance along the track between the points where they meet for the 3rd and 6th time?
- a)56 km
- b)62 km
- c)28 km
- d)42 km
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Rakesh and Vishal are running along a circular path of circumference 8...
Solution: 
The initial speeds of Rakesh and Vishal is in ratio 5 : 1 .
The distance covered by Rakesh and Vishal before meeting would be in the ratio 5 : 1 .
The distance covered by Rakesh and Vishal before meeting would be in the ratio 5 : 1 .
i.e. Rakesh will cover 70 km and Vishal will cover 14 km before their 1st meeting.
Now they will exchange their speeds and their directions.
Rakesh will travel at speed of 17 km/hr and Vishal will travel at a speed of 85 km/hr.
The distance covered by Vishal and Rakesh before meeting would be in the ratio 5 : 1 . Rakesh will cover 14 km and Vishal will cover 70 km between their 1st and 2nd meeting.
The distance between their meeting points will be 14 km. As they repeat the same process the distance between their meeting points will be a multiple of 14.
We are required to find the distance between their 3rd and 6th meeting (6th meeting will be at starting point).
The distance must be 3 x 14 = 42 km Hence, option 4.
Now they will exchange their speeds and their directions.
Rakesh will travel at speed of 17 km/hr and Vishal will travel at a speed of 85 km/hr.
The distance covered by Vishal and Rakesh before meeting would be in the ratio 5 : 1 . Rakesh will cover 14 km and Vishal will cover 70 km between their 1st and 2nd meeting.
The distance between their meeting points will be 14 km. As they repeat the same process the distance between their meeting points will be a multiple of 14.
We are required to find the distance between their 3rd and 6th meeting (6th meeting will be at starting point).
The distance must be 3 x 14 = 42 km Hence, option 4.
Most Upvoted Answer
Rakesh and Vishal are running along a circular path of circumference 8...
Key Information:
- Rakesh and Vishal are running along a circular path of circumference 84 km.
- They start from point O1 and meet for the first time at point O2.
- After meeting, they exchange their speeds as well as their directions and continue running around the track.
- They repeat this process every time they meet.
- Initially, Rakesh has a speed of 85 km/hr and Vishal has a speed of 17 km/hr.
Approach:
- We need to find the distance along the track between the points where they meet for the 3rd and 6th time.
- Let's find the time taken by Rakesh and Vishal to meet for the first time.
- Then we can determine the time taken for them to meet for the 3rd and 6th time by using the concept of relative speed.
- Finally, we can calculate the distance between the points where they meet for the 3rd and 6th time.
Detailed Solution:
The time taken by Rakesh and Vishal to meet for the first time can be calculated using the formula:
Time = Distance / Speed
For Rakesh, the distance is 84 km (the circumference of the circular path) and the speed is 85 km/hr.
So, the time taken by Rakesh to meet Vishal for the first time is:
Time taken by Rakesh = 84 km / 85 km/hr = 0.988 hours
Similarly, the time taken by Vishal to meet Rakesh for the first time is:
Time taken by Vishal = 84 km / 17 km/hr = 4.941 hours
Now, let's calculate the time taken for them to meet for the 3rd and 6th time.
When they meet for the 3rd time, Rakesh and Vishal would have covered a distance of 3 times the circumference of the circular path.
So, the time taken for them to meet for the 3rd time is:
Time taken for 3rd meeting = 3 * Time taken by Rakesh = 3 * 0.988 hours = 2.964 hours
Similarly, the time taken for them to meet for the 6th time is:
Time taken for 6th meeting = 6 * Time taken by Rakesh = 6 * 0.988 hours = 5.928 hours
Now, we can calculate the distance between the points where they meet for the 3rd and 6th time using the formula:
Distance = Speed * Time
For Rakesh, the speed is 85 km/hr and the time taken is 5.928 hours.
So, the distance
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Rakesh and Vishal are running along a circular path of circumference 84 km in opposite directions. They start from point O1and meet for the first time at point O2.After meeting they exchange their speeds as well as their directions and continue running around the track. They repeat this process every time they meet. Initially, Rakesh has a speed of 85 km/hr and Vishal has a speed of 17 km/hr. What is the distance along the track between the points where they meet for the 3rd and 6th time?a)56 kmb)62 kmc)28 kmd)42 kmCorrect answer is option 'D'. Can you explain this answer?
Question Description
Rakesh and Vishal are running along a circular path of circumference 84 km in opposite directions. They start from point O1and meet for the first time at point O2.After meeting they exchange their speeds as well as their directions and continue running around the track. They repeat this process every time they meet. Initially, Rakesh has a speed of 85 km/hr and Vishal has a speed of 17 km/hr. What is the distance along the track between the points where they meet for the 3rd and 6th time?a)56 kmb)62 kmc)28 kmd)42 kmCorrect answer is option 'D'. 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 Rakesh and Vishal are running along a circular path of circumference 84 km in opposite directions. They start from point O1and meet for the first time at point O2.After meeting they exchange their speeds as well as their directions and continue running around the track. They repeat this process every time they meet. Initially, Rakesh has a speed of 85 km/hr and Vishal has a speed of 17 km/hr. What is the distance along the track between the points where they meet for the 3rd and 6th time?a)56 kmb)62 kmc)28 kmd)42 kmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rakesh and Vishal are running along a circular path of circumference 84 km in opposite directions. They start from point O1and meet for the first time at point O2.After meeting they exchange their speeds as well as their directions and continue running around the track. They repeat this process every time they meet. Initially, Rakesh has a speed of 85 km/hr and Vishal has a speed of 17 km/hr. What is the distance along the track between the points where they meet for the 3rd and 6th time?a)56 kmb)62 kmc)28 kmd)42 kmCorrect answer is option 'D'. Can you explain this answer?.
Rakesh and Vishal are running along a circular path of circumference 84 km in opposite directions. They start from point O1and meet for the first time at point O2.After meeting they exchange their speeds as well as their directions and continue running around the track. They repeat this process every time they meet. Initially, Rakesh has a speed of 85 km/hr and Vishal has a speed of 17 km/hr. What is the distance along the track between the points where they meet for the 3rd and 6th time?a)56 kmb)62 kmc)28 kmd)42 kmCorrect answer is option 'D'. 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 Rakesh and Vishal are running along a circular path of circumference 84 km in opposite directions. They start from point O1and meet for the first time at point O2.After meeting they exchange their speeds as well as their directions and continue running around the track. They repeat this process every time they meet. Initially, Rakesh has a speed of 85 km/hr and Vishal has a speed of 17 km/hr. What is the distance along the track between the points where they meet for the 3rd and 6th time?a)56 kmb)62 kmc)28 kmd)42 kmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rakesh and Vishal are running along a circular path of circumference 84 km in opposite directions. They start from point O1and meet for the first time at point O2.After meeting they exchange their speeds as well as their directions and continue running around the track. They repeat this process every time they meet. Initially, Rakesh has a speed of 85 km/hr and Vishal has a speed of 17 km/hr. What is the distance along the track between the points where they meet for the 3rd and 6th time?a)56 kmb)62 kmc)28 kmd)42 kmCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Rakesh and Vishal are running along a circular path of circumference 84 km in opposite directions. They start from point O1and meet for the first time at point O2.After meeting they exchange their speeds as well as their directions and continue running around the track. They repeat this process every time they meet. Initially, Rakesh has a speed of 85 km/hr and Vishal has a speed of 17 km/hr. What is the distance along the track between the points where they meet for the 3rd and 6th time?a)56 kmb)62 kmc)28 kmd)42 kmCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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