Train Crossing a Stationary Object or Man MCQ Quiz - Objective Question with Answer for Train Crossing a Stationary Object or Man - Download Free PDF

Calculation

Let length of train A and train B is 2x and x respectively.

So, [2x +x]/2 = 1500

Or, 3x = 3000

Or, x = 1000

So, Length of train A is 2000 and length of train B 1000.

Speed of train B is 1000/10 = 100 m/sec

Speed of train A is 100/2 = 50 m/sec

So, required time = [2000/50] = 40 sec

Given:

Length of the train = 800 m

Speed of the train = 126 kmph

Time to cross the tunnel = 61 seconds

Formula Used:

Total Distance = Length of the train + Length of the tunnel

Speed = Distance / Time

Calculation:

Convert speed to m/s: Speed = 126 × (1000 / 3600)

⇒ Speed = 126 × (10 / 36)

⇒ Speed = 35 m/s

Distance covered in 61 seconds: Distance = Speed × Time

⇒ Distance = 35 × 61

⇒ Distance = 2135 m

Length of the tunnel = Distance - Length of the train

⇒ Length of the tunnel = 2135 - 800

⇒ Length of the tunnel = 1335 m

The length of the tunnel is 1335 m.

Given:

Speed of the train = 54 km/h

Time taken to pass the platform = 36 seconds

Time taken to pass a man = 20 seconds

Formula Used:

Length of the train = Speed × Time taken to pass a man

Length of the platform = Speed × Time taken to pass the platform - Length of the train

Calculation:

Speed in m/s = 54 × (1000 / 3600) = 15 m/s

Length of the train = 15 × 20 = 300 m

Length of the platform = 15 × 36 - 300

⇒ Length of the platform = 540 - 300

⇒ Length of the platform = 240 m

The correct answer is option 2.

Given:

Length of train = 130 m

Speed of train = 45 km/hr

Time to cross = 30 sec

Formula used:

Speed = Distance / Time

Distance = Length of train + Length of bridge

Calculation:

Convert speed to m/sec: 45 km/hr = 45 × (1000/3600) m/sec

⇒ 45 × (5/18) m/sec

⇒ 225/18 m/sec

⇒ 12.5 m/sec

Distance = Speed × Time

⇒ 12.5 × 30 m

⇒ 375 m

Distance = Length of train + Length of bridge

⇒ 375 = 130 + Length of bridge

⇒ Length of bridge = 375 - 130

⇒ Length of bridge = 245 m

∴ The length of the bridge is 245 m.

Given:

The length of the railway bridge = 120 m

Formula used:

Let the length of the train be L meters and speed of the train be S m/s

Speed (S) = Distance / Time

Calculation:

When train crosses the man, it covers its own length:

⇒ S = L / 6

When train crosses the bridge, it covers its own length plus the length of the bridge:

⇒ S = (L + 120) / 10

Equating both speed equations:

⇒ L / 6 = (L + 120) / 10

⇒ 10L = 6(L + 120)

⇒ 10L = 6L + 720

⇒ L = 180 m

Now, substitute L into S = L / 6:

⇒ S = 180 / 6 = 30 m/s

Convert speed into km/h:

⇒ Speed = 30 × 18 / 5 = 108 km/h

∴ The length of the train is 180 m and its speed is 108 km/h. The correct answer is option (3).

Let the speed of the train be x m/s.

Given length of the train = 500 m

Length of the tunnel = 1000 m

Time taken to pass the tunnel = 1 minute = 60 seconds

∴ x = (500 + 1000) ÷ 60

x = 25 m/s

Speed of the train in km/hr =\(\;25 \times \frac{{18}}{5}\frac{{km}}{{hr}}\)

∵ The ratio of speeds of two trains is 4 : 7;

Suppose the speed of the trains are 4x & 7x respectively;

∵ Both the trains can cross a pole in 12 seconds;

∴ Length of 1^st train = 4x × 12 = 48x

Length of 2^nd train = 7x × 12 = 84x

Given:

Speed of train B is 18km/h more than that of train A.

Length of train A is 210m less than that of train B.

Calculation:

Let D is the length of train A and the speed of train A be x m/s.

Then length of train B = D + 210

And the speed of train B is 18 km/h(18 × 5/18 = 5 m/s) more than the speed of train A.

Speed of train B = (x + 5) m/s

Train A crosses a pole in 32 seconds,

32 = D/x

⇒ x = D/32  ...... (i)

Both trains cross each other in 34 seconds

34 = (D + D + 210)/(x + x + 5) = (2D + 210)/(2x+5)

From (i),

⇒ 34 = (2D + 210)/(2 × D/32 +5)

⇒ 34 = (2D + 210)/(D/16 + 5)

⇒ 34 × (D/16 + 5) = 2D + 210

⇒ 34D + 16 × 170 = 32D +  16 × 210

⇒ 34D - 32D = 16 × 210 - 16 × 170

⇒ 2D = 16 × 40

⇒ D = 320 m. 

Formula Used:

Time taken = Distance/Speed

Calculation:

Let the length of the train be x

\(\Rightarrow {\rm{}}\frac{{600\; + \;x}}{{50}} = \frac{{900\; +\; x}}{{60}}\)

⇒ 3600 + 6x = 4500 + 5x

⇒ x = 900 metres

\(\Rightarrow {\rm{}}Speed = \frac{{600\; + \;900}}{{50}} = 30\;m/sec.\)

⇒ Speed = 30 × 18/5 = 108 km/h

∴ The length and speed of the train are 900 metres and 108 km/h.

Additional Information

1 km/hr = 5/18 m/sec 

The distance between two stations, A and B = 575 km,

Speed of first train = 50 km/hr

Speed of second train = 60 km/hr

Distance covered by first train in 30 min (1/2 hr) = 50 × 1/2 = 25 km

Remaining distance = 575 - 25 = 550 km

Relative speed, if opposite direction = 50 + 60 = 110 km/hr

As we know,

Time = Distance/speed

Both train meet each other in = 550/110 = 5 hrs

Distance covered in 5 hrs by first train = 5 × 50 = 250 km

Total distance covered by first train = 25 + 250 = 275 km

Both trains meet each other 275 km far from station A.

Given

Length of train = 330 meters

The train crosses a 550 meters long bridge in 11 seconds

Formula used:

Time = Distance/Speed

Solution:

Speed of train = (330 + 550)/11 = 880/11

Time taken to cross the second bridge = (330 + 570)/880 × 11 = (45/4) seconds

Therefore, the train takes (45/4) the seconds to cross a 570 meters long bridge.

Given:

Length of the train = 120 m

Speed of the train = 60 km/h

Time taken to cross the bridge = 18 seconds

Formula used:

Speed = Distance/Time

Solution:

Let the length of the bridge be x.

Speed = 60 km/h = 60 × 5/18 m/s

Time = 18 s

Distance = Speed ×  Time = 60 × 5/18 × 18 s = 300 m

300 m = 120 m + x

x = 300 m - 120 m

x = 180 m

Therefore, the length of the bridge is 180 m.

Formula:

Let t be the time taken by A and B to cross each other

Let t1 and t2 be the times taken by A and B respectively to reach their destinations after crossing each other

 Then, t² = t1 × t2

Calculation:

Here, t = 4 hours

t1 = 10 hours

Time taken by train A after meeting =10 - 4 = 6 hours

⇒ 4² = 6 × t2

⇒ 16 = 6 × t2

⇒ t2 = 2.67

∴ Total time taken by B to travel XY = 4 + 2.7 = 6.67 hours

Concept:

When two bodies run in the opposite direction, then their relative velocities get added.

1 km/hr = 5/18 m/s.

1 m/s = 18/5 km/hr.

Calculation:

Length of train = 220 m, Speed of train = 54 km/hr ⇒ 15 m/s and Speed of man = 12 km/hr ⇒ 10/3 m/s [ 1 km/hr = 5/18 m/s]

\(Time = \frac{Distance}{Speed}\)

⇒ \(\frac{220}{\frac{10}{3}\;+\;15} \)   -----(Speed gets added due to different direction)

\(⇒ \frac{220\;\times\;3}{55}\)

⇒ 12 sec.

Given:

Speed of the two trains is 80 km/h and 90 km/h

They cross each other in 3 minutes

Concept used:

Time = Distance/speed

Relative speed = When two bodies moving in the same direction then their relative speed of them will be different of the individual speed

Calculation:

3 min = 180 sec

The relative speed of the trains = 90 - 80

⇒ 10 km/h

Speed in m/sec = 10 × (5/18)

⇒ 25/9

Let the length of the other train be x m

Now,

[(230 + x)/(25/9)] = 180

⇒ (230 + x) = 180 × (25/9)

⇒ 230 + x = 500

⇒ x = 270

So, length of the other train = 270 m

∴ The length (in m) of the other train is 270.