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Ram, Akash and Shyam are Marathon runners. Ram and Shyam start running towards each other from two ends, say R and S, of a straight track of length 20 km, Akash in turn starts running from midpoint of R and S at the same time towards Shyam i.e., towards S and after reaching S, he immediately turns and starts running towards R with the same speed. Akash and Shyam meet for the first time after 1 hour and Akash and Ram meet for the first time after further 3 hours. If Ram and Shyam both start running from the same end towards the other end after how much time will the distance between them will be 5 km?
  • a)
    45 minutes
  • b)
    1 hour
  • c)
    1.5 hours
  • d)
    2 hours
  • e)
     Speed of both Ram and Shyam is same so the distance between them cannot be 5 km.
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Ram, Akash and Shyam are Marathon runners. Ram and Shyam start running...
The distance between R and S is 20 km.
Let speed of Ram, Akash and Shyam be a, b, and c km/hr respectively.
Shyam and Akash travel in the opposite direction at (b + c)km/hr.
Shyam and Akash meet each other after 1 hour and together they cover a distance of 10km.
10 = 1 x(b + c)...( i)
Ram and Akash travel in the opposite direction at (a + b)km/hr.
Ram and Akash meet each other after 1+3 = 4 hours and together they cover a distance of 20 + 10 = 30 km.
​30 = 4 x (a + b)... (ii)
Subtracting (ii) from four times (i) we get c-a = 2.5
If Ram and Shyam travel in the same direction, relative speed = (c - a)km/hr = 2.5 km/hr
2.5
Hence, option 4.
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Most Upvoted Answer
Ram, Akash and Shyam are Marathon runners. Ram and Shyam start running...
To solve this problem, let's break it down step by step:

1. Akash and Shyam meet for the first time after 1 hour.
2. Akash and Ram meet for the first time after an additional 3 hours.
3. We need to find the time it takes for Ram and Shyam to be 5 km apart.

Let's assume the speed of Akash, Ram, and Shyam to be x km/h.

Meeting of Akash and Shyam:
- Akash and Shyam start running towards each other from opposite ends.
- They meet after 1 hour, which means they have covered a total distance of 20 km (the length of the track).
- Since they meet in 1 hour, their combined speed is 20 km/h (20 km in 1 hour).
- Since Akash starts from the midpoint of R and S, he has covered 10 km in 1 hour.
- This means that Shyam has also covered 10 km in 1 hour.
- Therefore, their combined speed is 20 km/h, which is equal to 2x (Akash's speed) + x (Shyam's speed).
- Simplifying this equation, we get 2x + x = 20.
- Solving for x, we find that x = 5 km/h.

Meeting of Akash and Ram:
- Akash and Ram meet after an additional 3 hours.
- In these 3 hours, Akash has covered a distance of 3 * 5 = 15 km (since his speed is 5 km/h).
- This means that Ram has also covered 15 km in 3 hours.
- Therefore, the distance between Akash and Ram at this point is 20 - 15 = 5 km.

Finding the time for Ram and Shyam to be 5 km apart:
- Ram and Shyam start running towards each other from the same end (either R or S).
- Since they both have the same speed of 5 km/h, their relative speed is 2 * 5 = 10 km/h.
- The distance between them is initially 20 km.
- We need to find the time it takes for them to be 5 km apart.
- Using the formula time = distance / speed, we have time = 5 / 10 = 0.5 hours = 30 minutes.

Therefore, the correct answer is option D) 2 hours.
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Ram, Akash and Shyam are Marathon runners. Ram and Shyam start running towards each other from two ends, say R and S, of a straight track of length 20 km, Akash in turn starts running from midpoint of R and S at the same time towards Shyam i.e., towards S and after reaching S, he immediately turns and starts running towards R with the same speed. Akash and Shyam meet for the first time after 1 hour and Akash and Ram meet for the first time after further 3 hours. If Ram and Shyam both start running from the same end towards the other end after how much time will the distance between them will be 5 km?a)45 minutesb)1 hourc)1.5 hoursd)2 hourse)Speed of both Ram and Shyam is same so the distance between them cannot be 5 km.Correct answer is option 'D'. Can you explain this answer?
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Ram, Akash and Shyam are Marathon runners. Ram and Shyam start running towards each other from two ends, say R and S, of a straight track of length 20 km, Akash in turn starts running from midpoint of R and S at the same time towards Shyam i.e., towards S and after reaching S, he immediately turns and starts running towards R with the same speed. Akash and Shyam meet for the first time after 1 hour and Akash and Ram meet for the first time after further 3 hours. If Ram and Shyam both start running from the same end towards the other end after how much time will the distance between them will be 5 km?a)45 minutesb)1 hourc)1.5 hoursd)2 hourse)Speed of both Ram and Shyam is same so the distance between them cannot be 5 km.Correct answer is option 'D'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Ram, Akash and Shyam are Marathon runners. Ram and Shyam start running towards each other from two ends, say R and S, of a straight track of length 20 km, Akash in turn starts running from midpoint of R and S at the same time towards Shyam i.e., towards S and after reaching S, he immediately turns and starts running towards R with the same speed. Akash and Shyam meet for the first time after 1 hour and Akash and Ram meet for the first time after further 3 hours. If Ram and Shyam both start running from the same end towards the other end after how much time will the distance between them will be 5 km?a)45 minutesb)1 hourc)1.5 hoursd)2 hourse)Speed of both Ram and Shyam is same so the distance between them cannot be 5 km.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ram, Akash and Shyam are Marathon runners. Ram and Shyam start running towards each other from two ends, say R and S, of a straight track of length 20 km, Akash in turn starts running from midpoint of R and S at the same time towards Shyam i.e., towards S and after reaching S, he immediately turns and starts running towards R with the same speed. Akash and Shyam meet for the first time after 1 hour and Akash and Ram meet for the first time after further 3 hours. If Ram and Shyam both start running from the same end towards the other end after how much time will the distance between them will be 5 km?a)45 minutesb)1 hourc)1.5 hoursd)2 hourse)Speed of both Ram and Shyam is same so the distance between them cannot be 5 km.Correct answer is option 'D'. Can you explain this answer?.
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