Problem on Trains MCQ Quiz - Objective Question with Answer for Problem on Trains - 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

Given:

Speed of the train = 90 km/hr = (90 × 1000) / 3600 = 25 m/s

Time taken to pass the man = 10 seconds

Time taken to pass the bridge = 18 seconds

Formula Used:

Total Length of Train + Length of Bridge = Speed × Time to pass the bridge

Length of Train = Speed × Time to pass the man

Calculation:

Length of Train = Speed × Time to pass the man

⇒ Length of Train = 25 × 10

⇒ Length of Train = 250 m

Total Length of Train + Length of Bridge = Speed × Time to pass the bridge

⇒ 250 + Length of Bridge = 25 × 18

⇒ 250 + Length of Bridge = 450

⇒ Length of Bridge = 450 - 250

⇒ Length of Bridge = 200 m

The length of the bridge is 200 m.

Given:

Length of train = 450 m

Speed of train = 65 km/hr

Time taken to cross man = 27 sec

Formula used:

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

If moving in same direction: Relative speed = Train speed − Man speed

If opposite direction: Relative speed = Train speed + Man speed

Calculations:

Relative speed = \(\frac{450}{27} \times \frac{18}{5} = 60\) kmph

Let man's speed be x kmph

If same direction: \(65 - x = 60\)

⇒ \(x = 65 - 60 = 5\) kmph

If the opposite direction: \(65 + x = 60\)

⇒ \(x = 60 - 65 = -5\) kmph

Negative speed is not possible. So, the man is moving in the same direction as the train at 5 km/hr.

∴ The correct answer is Option (3).

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

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 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.

Given:-

Train₁= 152.5m

Train₂= 157.5m

Time = 9.3 sec

Calculation:-

⇒ Total distance to be covered = total length of both the trains

= 152. 5 + 157.5

= 310 m

Total time taken = 9.3 sec

Speed = distance/time

= (310/9.3) m/sec

= (310/9.3) × (18/5)

= 120 km/hr

∴ The combined speed of the two trains every hour would then be 120 km/hr.

Alternate Method When two trains are moving in opposite direction-

Let the speed of ine is 'v' and the second is 'u'

∴ Combined speed = v + u

Total distance = 152.5 + 157.5

= 310 m

∴ Combined speed = Total distance/total time

⇒ (v + u) = 310/9.3

⇒ (v + u) = 33.33 m/s

⇒ (v + u) = 33.33 × (18/5)

⇒ (v + u) = 120 km/hr

Given:

Two trains are running on opposite tracks between stations A and B.

After crossing each other they take 4 hr and 9 hr respectively to reach their destination.

Speed of first train is 54 kmph.

Formula used:

After crossing each other, if time taken by 2 trains is T1 and T2 resp. then, S1/S2 = √T2/√T1

where, S1 and S2 are speeds of first and second train respectively

Calculation:

We have, T1 = 4hr, T2 = 9hr, S1 = 54 kmph

⇒ 54/ S2 = √[9/4] = 3/2

⇒ S2 = 54 × 2 × 1/3 = 36 kmph

⇒ Speed of second train = 36 kmph

Alternate Method

Let the speed of the second train be 'x' kmph

Also, time taken to cross each other = √(T1 × T2) = √(9 × 4) = 6 hrs 

Total distance = 54 × 6 + x × 6 = x × 9 + 54 × 4

⇒ 9x - 3x = 54 × (6 - 2)

⇒ 6x = 216

⇒ x = 36 kmph = Speed of second train 

Given:

Train A takes 13 seconds to cross a pole.

Train B takes 26 seconds to cross a pole.

Concept:

Speed = Distance / Time

When two trains are moving in the same direction, their relative speed is the difference of their speeds.

Solution:

Let the length of each train be L.

⇒ Speed of train A = L/13, speed of train B = L/26.

When the two trains cross each other, the total distance covered is 2L (length of train A + length of train B).

Relative speed of the two trains = speed of train A - speed of train B = L/13 - L/26 = L/26.

Time taken to cross each other = total distance / relative speed = 2L / (L/26) = 52 seconds.

Hence, the two trains take 52 seconds to cross each other.

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:

Two train running towards each-other at the speed of 50 km/hr and 60 km/hr.

Two trains meet each other, the second train covered 120 km more distance than first train.

Formula used:

Speed × time = distance

Calculations:

Let the two trains meet after x hours.

Then, 60x − 50x = 120

⇒10x = 120

⇒x = 12hrs

Distance = (Distance covered by slower train) + (Distance covered by faster train) = [(50 × 12) + (60 × 12)] km

= 600km + 720km = 1320 km

∴ The answer is 1320 km

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 =\(\;25 \times \frac{{18}}{5}\frac{{km}}{{hr}}\)

Shortcut Trick

We can solve this question by applying the allegation method.

Thus,

Ratio of their speed = 14 : 4 = 7 : 2

∴ The correct answer is option (1).

Alternate Method

Given:

Train one crosses a man in 28 seconds

Train two crosses the man in 10 seconds

They both cross each other in 24 seconds

Formula used:

Time = Distance/ speed

As the trains travel in opposite directions, the speed of the trains added

Calculation:

Let the speed of the first train & second train be x m/s and y m/s respectively.

Length of the first train is 28x metres

Length of the second train is 10y meters

According to the question,

⇒ 24 = (28x + 10y) / (x + y)

⇒ 24x + 24y = 28x + 10y

⇒ 14y = 4x

⇒ x/y = 7/2

∴ The ratio of the speed of the train is 7 : 2.

Given:

Train covers first half of the distance at 3 kmph and second half of the distance at 6 kmph.

Formula used:

When distance is equal, Average speed = [2 × S1 × S2] / [S1 + S2]

Calculation:

Average speed = (2 × 3 × 6)/(3 + 6)

⇒ 36 / 9

⇒ 4 kmph

∴ The average speed is 4 kmph

Alternate Method

Let total distance be 36 km.

Time taken to cover 1st half distance = 18/3 = 6 hr

Time taken to cover 2nd half distance = 18/6 = 3 hr

∴ Average speed = Total distance/Total time = 36/(6 + 3) = 36/9 = 4 km/h