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11. A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

A. 230 m

B. 240 m

C. 260 m

D. 320 m

Discuss

Solution:

\begin{aligned} Relative speed \\ = (120 + 80) km/hr \\ = 200 \times \frac{5}{18} m/sec \\ = \frac{500}{9} m/sec \\ Let the length of the other train be x metres . \\ Then, \frac{x + 270}{9} = \frac{500}{9} \\ \Rightarrow x + 270 = 500 \\ \Rightarrow x = 230 \end{aligned}

12. A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

A. 230 m

B. 240 m

C. 260 m

D. 270 m

Discuss

Solution:

\begin{aligned} Speed = 72 \times \frac{5}{18} m/sec \\ = 20 m/sec \\ Time = 26 sec \\ Let the length of the train be x metres . \\ Then, \frac{x + 250}{26} = 20 \\ \Rightarrow x + 250 = 520 \\ \Rightarrow x = 270 \end{aligned}

13. Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:

A. 30 km/hr

B. 45 km/hr

C. 60 km/hr

D. 75 km/hr

Discuss

Solution:

\begin{aligned} Let the speed of the slower train be x m/sec \\ Then, speed of the faster train = 2 x m/sec \\ Relative speed = (x + 2 x) m/sec = 3 x m/sec \\ ∴ \frac{100 + 100}{8} = 3 x \\ \Rightarrow 24 x = 200 \\ \Rightarrow x = \frac{25}{3} \\ So, speed of the faster train = \frac{50}{3} m/sec \\ = \frac{50}{3} \times \frac{18}{5} km/hr \\ = 60 km/hr \end{aligned}

14. Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:

A. 9

B. 9.6

C. 10

D. 10.8

Discuss

Solution:

\begin{aligned} Relative speed = (60 + 40) km/hr \\ = 100 \times \frac{5}{18} m/sec \\ = \frac{250}{9} m/sec . \\ Distance covered in crossing each other \\ = (140 + 160) m = 300 m \\ Required time \\ = 300 \times \frac{9}{250} sec \\ = \frac{54}{5} sec \\ = 10.8 sec \end{aligned}

15. A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

A. 5 sec

B. 6 sec

C. 7 sec

D. 10 sec

Discuss

Solution:

\begin{aligned} Speed of train relative to man \\ = (60 + 6) km/hr \\ = 66 km/hr \\ = 66 \times \frac{5}{18} m/sec \\ = \frac{55}{3} m/sec \\ ∴ Time taken to pass the man \\ = 110 \times \frac{3}{55} sec = 6 sec \end{aligned}

16. A train travelling at a speed of 75 mph enters a tunnel 3 ¹/₂ miles long. The train is ¹/₄ mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

A. 2.5 min

B. 3 min

C. 3.2 min

D. 3.5 min

Discuss

Solution:

\begin{aligned} Total distance covered \\ = (\frac{7}{2} + \frac{1}{4}) miles \\ = \frac{15}{4} miles \\ ∴ Time taken \\ = (\frac{15}{4 \times 75}) hrs \\ = \frac{1}{20} hrs \\ = (\frac{1}{20} \times 60) min \\ = 3 min \end{aligned}

17. A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:

A. 130

B. 360

C. 500

D. 540

Discuss

Solution:

\begin{aligned} Speed = (78 \times \frac{5}{18}) m/sec \\ = \frac{65}{3} m/sec \\ Time = 1 minute = 60 second . \\ Let the length of the tunnel be x metres . \\ Then, \frac{800 + x}{60} = \frac{65}{3} \\ \Rightarrow 3 (800 + x) = 3900 \\ \Rightarrow x = 500 \end{aligned}

18. A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?

A. 320 m

B. 350 m

C. 650 m

D. Data inadequate

Discuss

Solution:

\begin{aligned} Speed = \frac{300}{18} m/sec \\ = \frac{50}{3} m/sec \\ Let the length of the platform be x metres . \\ Then, \frac{x + 300}{39} = \frac{50}{3} \\ \Rightarrow 3 (x + 300) = 1950 \\ \Rightarrow x = 350 m . \end{aligned}

19. A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

A. 50 m

B. 150 m

C. 200 m

D. Data inadequate

Discuss

Solution:

\begin{aligned} Let the length of the train be x metres \\ and its speed by y m/sec \\ T h e n, \frac{x}{y} = 15 \Rightarrow y = \frac{x}{15} \\ ∴ \frac{x + 100}{25} = \frac{x}{15} \\ \Rightarrow 15 (x + 100) = 25 x \\ \Rightarrow 15 x + 1500 = 25 x \\ \Rightarrow 1500 = 10 x \\ \Rightarrow x = 150 m \end{aligned}

20. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

A. 69.5 km/hr

B. 70 km/hr

C. 79 km/hr

D. 79.2 km/hr

Discuss

Solution:

\begin{aligned} Let the length of the train be x metres \\ and its speed by y m/sec \\ Then, \frac{x}{y} = 8 \Rightarrow x = 8 y \\ Now, \frac{x + 264}{20} = y \\ \Rightarrow 8 y + 264 = 20 y \\ \Rightarrow y = 22 \\ ∴ Speed = 22 m/sec \\ = 22 \times \frac{18}{5} km/hr \\ = 79.2 km/hr \end{aligned}

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