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

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

Calculations:

Speed of Train A = Distance / Time = 80 m / 16 s = 5 m/s.

Since the speed of Train B is the same as Train A, the speed of Train B = 5 m/s.

Length of Train B = 3 × Length of Train A

⇒ 3 × 80 = 240 m.

Length of the platform = (1/2) × Length of Train A

⇒ (1/2) × 80 = 40 m.

To cross the platform, Train B needs to cover its own length plus the length of the platform, i.e., 240 m + 40 m = 280 m.

Time taken by Train B to cross the platform = Distance / Speed

⇒ 280 m / 5 m/s = 56 seconds.

∴ It would take Train B 56 seconds to cross the platform.

Given:

Speed of faster train = 90 km/h

Speed of slower train = 51 km/h

Time to cross = 36 seconds

Trains are of equal length and moving in the same direction

Formula used:

Relative Speed = (Speed₁ - Speed₂)

Distance = Relative Speed × Time

Length of each train = (Distance ÷ 2)

Calculation:

⇒ Relative Speed = 90 - 51 = 39 km/h

⇒ 39 km/h = 39 × (1000 ÷ 3600) = 10.83 m/s

⇒ Distance = 10.83 × 36 = 389.88 m

⇒ Length of each train = 389.88 ÷ 2 ≈ 194.94 m

∴ The length of each train is approximately 195 metres.

Given:

Length of the goods train = 350 m.

Length of the tunnel = 1250 m.

Time taken to pass through the tunnel = 80 sec.

Formula Used:

Speed = Total Distance / Time

Calculation:

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

Total Distance = 350 + 1250

Total Distance = 1600 m

Time = 80 sec

Speed = Total Distance / Time

Speed = 1600 / 80

Speed = 20 m/s

Convert m/s to km/hr:

Speed in km/hr = Speed in m/s × 18/5

Speed in km/hr = 20 × (18/5)

Speed in km/hr = 72 km/hr

The speed of the train is 72 km/hr.

Given:

Speed of train 1 (S₁) = 50 km/h

Speed of train 2 (S₂) = 110 km/h

Length of train 1 (L₁) = 500 m

Time to cross (t) = 12 seconds

Formula used:

Relative speed (opposite direction) = S₁ + S₂

Distance = Speed × Time

1 km/h = 5/18 m/s

When two trains cross each other, the total distance covered is the sum of their lengths.

Calculation:

Relative speed = 50 km/h + 110 km/h = 160 km/h

Convert relative speed to m/s:

⇒ 160 km/h = 160 × \(\frac{5}{18}\) m/s

⇒ Relative speed = \(\frac{800}{18}\) m/s = \(\frac{400}{9}\) m/s

Let the length of train 2 be L₂.

Total distance covered = L₁ + L₂ = 500 + L₂ meters

Using Distance = Speed × Time:

⇒ 500 + L₂ = \(\frac{400}{9}\) × 12

⇒ 500 + L₂ = \(\frac{400 \times 4}{3}\)

⇒ 500 + L₂ = \(\frac{1600}{3}\)

⇒ 500 + L₂ = 533.33

⇒ L₂ = 533.33 - 500

⇒ L₂ = 33.33

∴ The length of the other train is 33.33 m.

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