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

Train A length = x + 120, Train B (stationary) = x + 80

A crosses B in 40 sec at 20 m/s

→ Total length = 800 m

→ 2x + 200 = 800

→ x = 300

Train B length = 380 m

Train B crosses bridge in 23.4 sec at 25 m/s

Bridge length + train length = 23.4 × 25 = 585 m

→ Bridge length = 585 - 380 = 205 m

Given:

Length of train (L_train) = 70 metres

Length of bridge (L_bridge) = 105 metres

Speed of train (S) = 75 kmph

Formula used:

Total Distance (D) = Length of train + Length of bridge

Time (T) = \(\dfrac{\text{Total Distance}}{\text{Speed}}\)

Calculations:

⇒ S = 75 kmph = 75 × \(\dfrac{5}{18}\) m/s

⇒ S = \(\dfrac{25 \times 5}{6}\) m/s (dividing 75 and 18 by 3)

⇒ S = \(\dfrac{125}{6}\) m/s

⇒ Total Distance = L_train + L_bridge

⇒ Total Distance = 70 m + 105 m = 175 m

⇒ Time = \(\dfrac{\text{Total Distance}}{\text{Speed}}\)

⇒ Time = \(\dfrac{175}{\frac{125}{6}}\)

⇒ Time = \(\dfrac{175 \times 6}{125}\)

⇒ Time = \(\dfrac{7 \times 6}{5}\)

⇒ Time = \(\dfrac{42}{5}\) seconds = \(8 \frac{2}{5}\) sec

∴ The time taken by the train to cross the bridge is \(8 \frac{2}{5}\) seconds.

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.

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.

Given:
Speed of the train = 40 km/hr

Speed of the Person (while walking) = 8km/hr

Time taken = 12 hours

Formula used:

Time taken = Distance/Speed

Calculation:

Time taken by the train at a speed of 40 kmph + Time taken by walking at 8 kmph = 12 hours 

Let ‘d’ be the distance of one side travel

(d/40) + (d/8) = 12

⇒ (d + 5d)/40 = 12

⇒ d = (40 × 12)/6 = 80 kms

Given:

Speed of train = 90 km/h

Time to cross a standing man = 8 seconds.

Length of platform = 250 meters.

Formula used:

Distance = Speed × Time

Calculation:

According to the questions:

Speed of train = 90 km/h

⇒ 90 × (5/18) m/sec.

⇒ 25 m/sec

We know that the distance covered by a train to cross a standing object is the length of the train itself.

So, Distance (Length of the train) = Speed × Time

⇒ Length of train = 25 × 8 m

⇒ Length of train = 200 m.

When the train crosses the platform of length 250 m,

Total distance covered by train = (200 + 250) m

⇒ 450 m

Now, Time to cross the platform = Distance/Speed

⇒ Time to cross the platform = 450/25

⇒ Time to cross the platform = 18 seconds.

∴ The time taken to cross the platform is 18 seconds.

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