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There is a string of length 100 m running from east to west. 1000 ants are dropped onto the string. Assume that each ant lands on the string facing either the east or the west direction. As soon as they land, each ant starts moving in the direction which is being faced by it at 50 m/ min till it falls off the string. But if an ant collides with another ant coming from the opposite direction, both of them reverse their directions and proceed to move now in the opposite directions. Ants fall only at either of the ends of the string. What is the minimum time by which the string is definitely free of ants?
(2015)
  • a)
    1 min
  • b)
    2 min
  • c)
    200 min
  • d)
    Infinite time
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
There is a string of length 100 m running from east to west. 1000 ants...

Let's take there are two ants.
Considering worst possible case we can see easily the required time is same as the time taken by an ant to reach one extreme point to another extreme point.
Which will be same when there are 1000 ants.
i.e.maximum time = 
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Most Upvoted Answer
There is a string of length 100 m running from east to west. 1000 ants...
Problem Analysis:
- There are 1000 ants on a string of length 100 m.
- Each ant moves at a speed of 50 m/min in the direction it is facing.
- If two ants collide, they reverse their directions.
- Ants fall off the string at either end.
- We need to find the minimum time by which the string is definitely free of ants.

Key Observations:
- Since each ant moves at a constant speed, the only way for an ant to fall off the string is by reaching one of the ends.
- If an ant is moving towards the east end, it will fall off the string in 2 minutes (100 m / 50 m/min).
- Similarly, if an ant is moving towards the west end, it will also fall off the string in 2 minutes.
- If two ants collide, they reverse their directions. This means that if an ant is moving towards the east end and collides with an ant moving towards the west end, both ants will reverse their directions and start moving towards the west end.
- Similarly, if an ant is moving towards the west end and collides with an ant moving towards the east end, both ants will reverse their directions and start moving towards the east end.
- This implies that whenever two ants collide, they will always end up moving towards the same end of the string.

Solution:
- Since all the ants will eventually fall off the string, we need to find the minimum time by which all the ants have fallen off.
- The worst-case scenario is when all the ants are moving towards the same end of the string.
- In this case, the time taken for all the ants to fall off the string is equal to the time taken for the ant that is farthest from the end to reach the end.
- Since each ant moves at a speed of 50 m/min, the ant that is farthest from the end will take 2 minutes to reach the end.
- Therefore, the minimum time by which the string is definitely free of ants is 2 minutes.

Answer:
The minimum time by which the string is definitely free of ants is 2 minutes.
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Community Answer
There is a string of length 100 m running from east to west. 1000 ants...

Let's take there are two ants.
Considering worst possible case we can see easily the required time is same as the time taken by an ant to reach one extreme point to another extreme point.
Which will be same when there are 1000 ants.
i.e.maximum time = 
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There is a string of length 100 m running from east to west. 1000 ants are dropped onto the string. Assume that each ant lands onthe string facing either the east or the west direction. As soon as they land, each ant starts moving in the direction which is beingfaced by it at 50 m/ min till it falls off the string. But if an ant collides with another ant coming from the opposite direction, bothof them reverse their directions and proceed to move now in the opposite directions. Ants fall only at either of the ends of thestring. What is the minimum time by which the string is definitely free of ants?(2015)a)1 minb)2 minc)200 mind)Infinite timeCorrect answer is option 'B'. Can you explain this answer?
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