Two trains are travelling in the same direction at 40 kmph, and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 metres, what is the length of the second train?a)125 metresb)150 metresc)175 metresd)185 metresCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Given:
- Speed of the first train = 40 kmph
- Speed of the second train = 22 kmph
- The first train is 125 metres long

To find:
- Length of the second train

Let's solve this problem step by step:

1. Convert the speeds of the trains from kmph to m/s:
- Speed of the first train = 40 kmph = (40 * 1000) / 3600 = 40000 / 3600 = 100 / 9 m/s
- Speed of the second train = 22 kmph = (22 * 1000) / 3600 = 22000 / 3600 = 50 / 9 m/s

2. The trains pass each other completely in 1 minute, which is equal to 60 seconds.

3. When two objects are moving in the same direction, the relative speed is the difference between their individual speeds. In this case, the relative speed of the second train with respect to the first train is:
- Relative speed = Speed of the second train - Speed of the first train
- Relative speed = (50 / 9) - (100 / 9) = -50 / 9 m/s (negative sign indicates they are moving in the same direction)

4. The relative speed gives us the rate at which the second train overtakes the first train. To find the length of the second train, we need to calculate the distance covered by the second train in 60 seconds.

5. Distance = Speed * Time
- Distance = (-50 / 9) * 60
- Distance = -3000 / 9 meters
- Distance = -333.33 meters (negative sign indicates they are moving in the same direction)

6. Since distance cannot be negative, we take the absolute value of the distance to get the length of the second train.
- Length of the second train = |Distance| = |-333.33| = 333.33 meters

7. Rounding off to the nearest meter, the length of the second train is approximately 333 meters.

Therefore, the length of the second train is 333 meters, which is not one of the given options. Since none of the given options match the calculated length of the second train, it seems that there may be an error in the question or options.

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