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Home > Practice > Arithmetic Aptitude > Problems on Trains > Miscellaneous

1. A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?

A. 120 metres

B. 180 metres

C. 324 metres

D. 150 metres

Discuss

Solution:

\begin{aligned} Speed = (60 \times \frac{5}{18}) m/sec = \frac{50}{3} m/sec \\ Length of the train = (Speed \times Time) \\ ∴ Length of the train \\ = (\frac{50}{3} \times 9) m = 150 m \end{aligned}

2. A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

A. 45 km/hr

B. 50 km/hr

C. 54 km/hr

D. 55 km/hr

Discuss

Solution:

\begin{aligned} Speed of the train relative to man \\ = \frac{125}{10} m/sec \\ = \frac{25}{2} m/sec \\ = \frac{25}{2} \times \frac{18}{5} km/hr \\ = 45 km/hr \\ Let the speed of the train be x km/hr . \\ Then, relative speed = (x - 5) km/hr \\ ∴ x - 5 = 45 \\ \Rightarrow x = 50 km/hr \end{aligned}

3. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:

A. 200 m

B. 225 m

C. 245 m

D. 250 m

Discuss

Solution:

\begin{aligned} Speed = 45 \times \frac{5}{18} m/sec \\ = \frac{25}{2} m/sec \\ Time = 30 sec \\ Let the length of bridge be x metres \\ Then, \frac{130 + x}{30} = \frac{25}{2} \\ \Rightarrow 2 (130 + x) = 750 \\ \Rightarrow x = 245 m \end{aligned}

4. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

A. 1 : 3

B. 3 : 2

C. 3 : 4

D. None of these

Discuss

Solution:

\begin{aligned} Let the speeds of the two trains be x m/sec \\ and y m/sec respectively . \\ Then, length of the first train = 27 x metres, \\ and length of the second train = 17 y metres . \\ ∴ \frac{27 x + 17 y}{x + y} = 23 \\ \Rightarrow 27 x + 17 y = 23 x + 23 y \\ \Rightarrow 4 x = 6 y \\ \Rightarrow \frac{x}{y} = \frac{3}{2} \end{aligned}

5. A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

A. 120 m

B. 240 m

C. 300 m

D. None of these

Discuss

Solution:

\begin{aligned} Speed = 54 \times \frac{5}{18} m/sec = 15 m/sec \\ Length of the train = (15 \times 20) m = 300 m \\ Let the length of the platform be x metres \\ Then, \frac{x + 300}{36} = 15 \\ \Rightarrow x + 300 = 540 \\ \Rightarrow x = 240 m \end{aligned}

6. A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

A. 65 sec

B. 89 sec

C. 100 sec

D. 150 sec

Discuss

Solution:

\begin{aligned} Speed = \frac{240}{24} m/sec = 10 m/sec \\ ∴ Required time \\ = \frac{240 + 650}{10} sec . \\ = 89 s e c . \end{aligned}

7. 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:

A. 50 m

B. 72 m

C. 80 m

D. 82 m

Discuss

Solution:

\begin{aligned} Let the length of each train be x metres . \\ Then, distance covered = 2 x metres . \\ Relative speed \\ = (46 - 36) km/hr \\ = 10 \times \frac{5}{18} m/sec \\ = \frac{25}{9} m/sec \\ ∴ \frac{2 x}{36} = \frac{25}{9} \\ \Rightarrow 2 x = 100 \\ \Rightarrow x = 50 \end{aligned}

8. A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

A. 40 sec

B. 42 sec

C. 45 sec

D. 48 sec

Discuss

Solution:

\begin{aligned} Formula for converting from km/hr to m/s: \\ X km/hr = X \times \frac{5}{18} m/s \\ Therefore, Speed \\ = 45 \times \frac{5}{18} m/sec = \frac{25}{2} m/sec \\ Total distance to be covered \\ = (360 + 140) m = 500 m \\ Formula for finding Time \\ = \frac{Distance}{Speed} \\ ∴ Required time \\ = (\frac{500 \times 2}{25}) \sec \\ = 40 \sec . \end{aligned}

9. Two trains are moving in opposite directions @ 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

A. 36

B. 45

C. 48

D. 49

Discuss

Solution:

\begin{aligned} Relative speed = (60 + 90) km/hr \\ = 150 \times \frac{5}{18} m/sec \\ = \frac{125}{3} m/sec \\ Distance covered \\ = (1.10 + 0.9) k m \\ = 2 k m \\ = 2000 m \\ Required time \\ = 2000 \times \frac{3}{125} sec \\ = 48 s e c \end{aligned}

10. A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?

A. 3.6 sec

B. 18 sec

C. 36 sec

D. 72 sec

Discuss

Solution:

\begin{aligned} Speed of train relative to jogger \\ = (45 - 9) km/hr \\ = 36 km/hr \\ 36 \times \frac{5}{18} m/sec \\ = 10 m/sec \\ Distance to be covered \\ = (240 + 120) m \\ = 360 m \\ ∴ Time taken \\ = \frac{360}{10} sec \\ = 36 sec \end{aligned}

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