A train overtakes two persons who are walking in the same direction in which the train is going at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is?

Question

Question : Two trains are running at 40 km/h and 20 km/h, respectively, in the same direction. The fast train completely passes a man sitting in the slow train in 5 seconds. The length of the fast train is:
Option 1: $23\frac{2}{9}$m
Option 2: $27$ m
Option 3: $27\frac{7}{9}$m
Option 4: $23$ m

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Answer 1

2 kmph = (2 x 5/18) m/sec = 5/9 m/sec.

4 kmph = (4 x 5/18) m/sec = 10/9 m/sec.

Let the length of the train be x metres and its speed be y m/sec

Then (x/y-5/9) = 9 and (x/y-10/9) = 10

therefore 9y - 5 = x and 10(9y - 10) = 9x

9y-x=5 and 90y-9x=100

on solving we get x=50

Then the length of the train be 50 metres.

Hope this information is helpful.

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A train overtakes two persons who are walking in the same direction in which the train is going at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is?

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Question : Two trains are running at 40 km/h and 20 km/h, respectively, in the same direction. The fast train completely passes a man sitting in the slow train in 5 seconds. The length of the fast train is:
Option 1: $23\frac{2}{9}$m
Option 2: $27$ m
Option 3: $27\frac{7}{9}$m
Option 4: $23$ m

Question : Two trains 320 m and 205 m in length are running towards each other on parallel lines. One train runs at the rate of 70 kmph and the other train runs at the rate of 56 kmph. Find the time they will take to cross each other (in seconds).
Option 1: 10
Option 2: 20
Option 3: 12
Option 4: 15

Question : Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:
Option 1: 72 m
Option 2: 80 m
Option 3: 82 m
Option 4: 50 m

Question : Two trains of the same length are running on parallel tracks in the same direction at the speeds of 60 km/h and 90 km/h, respectively. The latter completely crosses the former in 30 seconds. The length of each train (in meters) is:
Option 1: 125
Option 2: 150
Option 3: 100
Option 4: 115