Towns A and B are 200 km apart; A is in the South and B in the North. There is only one railway track between them; on a certain day, trains start simultaneously from both A and B with different speeds towards each other. The train starting from A has a speed of 40 km/hr. A fly is initially 80 km north of A. As soon as the trains start, it starts flying towards the train initially at B; on reaching it, it immediately turns around and starts flying towards the other train, and turns around again on reaching it. It continues this behaviour till the trains meet and it is squashed. At the time that the trains meet, the fly has flown equal distances North and South. What is the speed (in km/hr) of the second train?a)30b)40c)50d)60Correct answer is option 'D'. Can you explain this answer?

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Towns A and B are 200 km apart; A is in the South and B in the North. There is only one railway track between them; on a certain day, trains start simultaneously from both A and B with different speeds towards each other. The train starting from A has a speed of 40 km/hr. A fly is initially 80 km north of A. As soon as the trains start, it starts flying towards the train initially at B; on reaching it, it immediately turns around and starts flying towards the other train, and turns around again on reaching it. It continues this behaviour till the trains meet and it is squashed. At the time that the trains meet, the fly has flown equal distances North and South. What is the speed (in km/hr) of the second train?

a)
30
b)
40
c)
50
d)
60

Correct answer is option 'D'. Can you explain this answer?

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Most Upvoted Answer

Towns A and B are 200 km apart; A is in the South and B in the North....

The fact that the fly has flown equal distances North and South shows that its final position is the same as its initial position; the point where the trains meet is 80 km from A.

The train starting from A has a speed of 40 km/hr, so it takes 2 hours to reach this point.

The other train must also take 2 hours to reach this same point, which is (200 - 80 =) 120 km from B, so the speed of the second train is 120/2 = 60 km/hr.

Hence, option 4.

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Towns A and B are 200 km apart; A is in the South and B in the North....

Let's break down the problem into smaller parts to understand it better.

1. Initial distances:
- Distance between Town A and Town B = 200 km
- Fly's initial position from Town A = 80 km north of A

2. Train speeds:
- Train starting from Town A = 40 km/hr

3. Fly's movement:
- The fly starts flying towards the train initially at Town B as soon as the trains start.
- On reaching the train at Town B, it immediately turns around and starts flying towards the other train.
- The fly continues this behavior until the trains meet.

We need to find the speed of the second train.

Let's assume:
- The speed of the second train = x km/hr
- The time taken for the trains to meet = t hours

Fly's movement:
- The fly starts flying towards the train at Town B, which is moving towards it with a speed of x km/hr.
- So, the relative speed between the fly and the train at Town B = (x + 40) km/hr
- The fly covers a distance of 80 km (initial distance) in t hours.

When the fly reaches the train at Town B:
- The train at Town B has traveled a distance of (x + 40) * t km.

Fly's movement after reaching the train at Town B:
- The fly turns around and starts flying towards the train at Town A, which is moving towards it with a speed of 40 km/hr.
- So, the relative speed between the fly and the train at Town A = (40 + 40) km/hr = 80 km/hr
- The fly covers a distance of 80 km (initial distance) in t hours.

When the fly reaches the train at Town A:
- The train at Town A has traveled a distance of 40 * t km.

At this point, the fly has flown equal distances north and south, which means:
- The distance covered in the north = 80 km
- The distance covered in the south = 80 km

Therefore, we can write the equation:
80 = (x + 40) * t + 40 * t

Simplifying the equation:
80 = xt + 40t + 40t
80 = xt + 80t
xt = 0
x = 0

Since x represents the speed of the second train, which cannot be zero, this is not possible.

Hence, there is no valid solution to this problem.

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Towns A and B are 200 km apart; A is in the South and B in the North. There is only one railway track between them; on a certain day, trains start simultaneously from both A and B with different speeds towards each other. The train starting from A has a speed of 40 km/hr. A fly is initially 80 km north of A. As soon as the trains start, it starts flying towards the train initially at B; on reaching it, it immediately turns around and starts flying towards the other train, and turns around again on reaching it. It continues this behaviour till the trains meet and it is squashed. At the time that the trains meet, the fly has flown equal distances North and South. What is the speed (in km/hr) of the second train?a)30b)40c)50d)60Correct 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 Towns A and B are 200 km apart; A is in the South and B in the North. There is only one railway track between them; on a certain day, trains start simultaneously from both A and B with different speeds towards each other. The train starting from A has a speed of 40 km/hr. A fly is initially 80 km north of A. As soon as the trains start, it starts flying towards the train initially at B; on reaching it, it immediately turns around and starts flying towards the other train, and turns around again on reaching it. It continues this behaviour till the trains meet and it is squashed. At the time that the trains meet, the fly has flown equal distances North and South. What is the speed (in km/hr) of the second train?a)30b)40c)50d)60Correct 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 Towns A and B are 200 km apart; A is in the South and B in the North. There is only one railway track between them; on a certain day, trains start simultaneously from both A and B with different speeds towards each other. The train starting from A has a speed of 40 km/hr. A fly is initially 80 km north of A. As soon as the trains start, it starts flying towards the train initially at B; on reaching it, it immediately turns around and starts flying towards the other train, and turns around again on reaching it. It continues this behaviour till the trains meet and it is squashed. At the time that the trains meet, the fly has flown equal distances North and South. What is the speed (in km/hr) of the second train?a)30b)40c)50d)60Correct answer is option 'D'. Can you explain this answer?.

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