Train Crossing a Platform MCQ Quiz - Objective Question with Answer for Train Crossing a Platform - Download Free PDF

Given:

Length of bridge = 150 meters

Train A takes 30 seconds to cross the bridge

Train B takes 15 seconds to cross the same bridge

Train A takes 15 seconds to cross a signal post

Both trains are of equal length

Calculation:

Let length of each train = L meters

Train A:

Time to cross bridge = 30 sec ⇒ Distance = L + 150

⇒ Speed of Train A = (L + 150) ÷ 30

Also, Train A crosses a signal post (length L) in 15 sec

⇒ Speed of Train A = L ÷ 15

Equating the two speeds:

(L + 150) ÷ 30 = L ÷ 15

⇒ (L + 150) = 2L

⇒ 150 = 2L - L = L

So, Length of each train = 150 meters

Speed of Train A:

⇒ Speed = L ÷ 15 = 150 ÷ 15 = 10 m/s

Speed of Train B:

Total distance Train B covers = L + 150 = 150 + 150 = 300 meters

Time = 15 seconds

⇒ Speed = 300 ÷ 15 = 20 m/s

When two trains cross each other in opposite directions:

Total distance = Sum of lengths = 150 + 150 = 300 meters

Relative speed = 10 + 20 = 30 m/s

Time = Distance ÷ Relative speed = 300 ÷ 30 = 10 seconds

Thus, teh correct answer is 10 seconds.

Calculation:

Speed of Train X = 72 km/h = 72  ×1000 / 3600 = 20 m/s

Train X crosses a bridge 1/3 of its own length in 20 seconds

Then it overtakes Train Y speed = 24 km/h = 6.67 m/s in 45 seconds

We have to find: Length of the bridge + Length of Train Y

Let the length of Train X = L meters.

Then the length of the bridge = L/3

Train X crosses the bridge

Time = 20 seconds

Speed = 20 m/s

So, total distance covered = 20 × 20 = 400 meters

Since it covers its own length + the bridge's length:

L + L/3 = 400

4L / 3 = 400

L = 400 × 3 / 4 = 300 m 

So:

Length of Train X = 300 m

Length of Bridge = 13 × 300 = 100 m

rain X overtakes Train Y:

Relative speed = 20 − (24 × 1000 / 3600) = 20 − 6.67 = 13.33 m/s

Time taken to overtake = 45 seconds

Distance covered = 13.33 × 45 = 600 meters

When Train X overtakes Train Y, it covers:

→ Its own length 300 m + Train Y's length = 600 m

⇒ Length of Train Y = 600 − 300 = 300 m 

Find sum of bridge and Train Y's lengths

Bridge = 100 m

Train Y = 300 m

Sum = 100 + 300 = 400 meters

Thus, the correct answer is 400 meters.

Calculation

Let speeds: A = 3x, B = 2x

Let length A = a

→ then B = 600 - a

Time = length / speed

→ a/3x - (600 - a)/2x = 3

We have two variable and only one equation. So, answer cannot be determined.  

Given:

Length of train = 350 m

Length of bridge = 250 m

Total time = 20 seconds

Formula used:

Speed = Total Distance / Time

Total Distance = Length of train + Length of bridge

Calculation:

Total Distance = 350 + 250 = 600 m

Speed (in m/s) = Total Distance / Time

⇒ Speed = 600 / 20

⇒ Speed = 30 m/s

Speed (in km/h) = (30 × 18) / 5

⇒ Speed = 108 km/h

∴ The correct answer is option (3).

Calculation

Let speed of train P and Q be 5x m/sec. & 9x m/sec. respectively

ATQ,

[ (d+300) / 5x] =  [(d+700) / 9x]

So, 9d + 2700 = 5d + 3500

So, 4d = 800

So, d = 200

Given:

Speed is 60 km per hour,

Train passed through a 1.5 km long tunnel in two minutes

Formula used:

Distance = Speed × Time

Calculation:

Let the length of the train be L

According to the question,

Total distance = 1500 m + L

Speed = 60(5/18)

⇒ 50/3 m/sec

Time = 2 × 60 = 120 sec

⇒ 1500 + L = (50/3)× 120

⇒ L = 2000 - 1500

⇒ L = 500 m

∴ The length of the train is 500 m.

Let the length of train be x m.

⇒ Speed of train = (length of platform + length of train)/time

According to question,

⇒ (110 + x)/ 13.5 = (205 + x)/18.25

⇒ (110 + x)/2.7 = (205 + x)/3.65

⇒ 401.5 + 3.65x = 553.5 + 2.7x

⇒ 0.95x = 152

⇒ x = 160

Given:

Length of a train is 1200m

Train took 120 sec to cross a tree

Length of a platform is 700m

Formula USed:

Speed = Distance/Time 

Calculation:

Speed = 1200/120 = 10 m/sec

Total distance = 1200 + 700 = 1900 m

Time = distance/speed = 1900/10 = 190 sec

∴ Time required to cross a platform is 190 sec.

Given:

Speed of the train = 72km/hr

The train passes the platform in 48 sec and the passenger in 30 sec

Concept used:

Speed = distance/time

While a train crossing a man it actually crossing it's own length.

Calculation:

Speed of the train is 72 km/hr = 72 × (5/18) = 20 m/sec

Length of train = speed × time

⇒ 20 × 30 = 600 m

Now, accordingly

\(20 = \;\frac{{x + 600}}{{48}}\)

⇒ \(20 × 48 = x + 600\)

⇒ x = 960 - 600

⇒ x = 360

∴ The length of the platform is 360 meter.

⇒ Speed = Distance/time

⇒ Speed of train = 36 × (5/18) = 10m/s

⇒ Distance covered in 53 seconds = 10 × 53 = 530 m

⇒ Length of train = 110m

Given:

A 250 meters long train crosses a bridge 750 meters long in 20 seconds

And crosses a platform in 15 seconds.

Formula Used:

Distance = Speed × Time

Calculation:

Let the speed of the train be S

And let the length of the platform be x

According to the question,

250 + 750 = S × 20

⇒ S = 1000/20

⇒ 50 m/sec

Now, Again according to the question

The train crosses the platform in 15 seconds

250 + x = 50 × 15

⇒ x = 750 - 250

⇒ x = 500 m

∴ The length of the platform is 500 m.

Given:

Time to cross the pole = 5 sec

Time to crosses the tunnel = 20 sec

Formula used:

Speed = Distance/Time

Calculation:

Let the length of the tunnel be x m and the length of the train be y m

Time = Distance/Speed

⇒ 5 = (y/90)

⇒ y = 450 m

Time to crosses the tunnel = Distance/Speed

⇒ 20 = (y + x)/90

⇒ 20 × 90 = (450 + x)

⇒ x = 1800 - 450 = 1350

∴ The length of the tunnel is 1350 m.

Formula used:

Speed = Distance / Time

(1 m/s) × (18/5) = 1 km/hr

Shortcut Trick

If train cross its length in 12 seconds and 170 m bridge in (36 - 12 = 24) seconds.

Speed of train = [170/24] × [18/5] = 25.5 km/hr

 Alternate Method

Let the length of the train be x m.

As we know,

Speed = Distance/time

Speed (v) = x/12     

x = 12 v                      -----(1)

Again,

v = (x + 170)/36          -----(2)

From equation (1)

v = (12v + 170)/36

⇒ 36v = 12v + 170

⇒ 24v = 170

⇒ v = 170/24 m/s 

⇒ v = (170/24) × (18/5) km/hr

Let length of train be A meter.

⇒ 70 kmph = 70 × 5/18 = 175/9 m/sec

A train crosses a 375 m long platform in 27 seconds,

⇒ 175/9 = (375 + A) /27

⇒ 375 + A = 175 × 3

⇒ A = 150

Given:

A train crosses a station platform in 36 seconds

And crosses a man standing on the platform in 20 seconds

The speed of the train is 54 km/h

Formula Used:

Speed = Distance/Time

Calculation:

Let the length of the train be x m and the length of the platform be y m 

According to the question

54 × (5/18) = x/20

⇒ 15 × 20 = x

⇒ x = 300 m

Again, According to the question

⇒ 54 × (5/18) = (300 + y) /36

⇒ 15 × 36 = 300 + x

⇒ y = 540 – 300

⇒ y = 240

∴ The length of the platform is 240.

Shortcut Trick As given train cross its length in 20 seconds.

So the train cross the platform in = 36 – 20 = 16 seconds

The distance covered by train in 16 seconds = 54 × (5/18) × 16 = 240