Did you know that solving train math problems questions can help you become a master of aptitude? These questions are a bit different from the basic speed, distance, and time problems you've seen before. Get ready to use your problem-solving skills and discover a whole new approach to solving train problems questions. You can also find Train problems below where it will be very useful for students looking for the right way to solve them.

Types of Train problems questions

These are the main type of questions which may be asked from the train-based problems:

Type	Given	To Find
Type 1 (Pole Tree, Man standing)	Speed of Train, Time to cover distance, Length of Train (Any 2 values Given)	3rd value
Type 2 (Bridge Platform etc.)	Length of Bridge, Length of Train, Time to cover Bridge, Speed of Train (Any 3 values Given)	4th value
Type 3	2 Trains same direction	Speed/ Length of any Train
Type 4	2 Trains opposite direction	Speed/ Length of any Train

Important Train problems questions Formulas

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Distance = Speed * Time

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Speed = Distance/Time

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Time = Distance/Speed

km/hr to m/s conversion: a km/hr = (a*5/18) m/s
mls to km/hr conversion: a m/s = (a*18/5) km/hr
Time taken by a train of length/metres to pass a pole or standing man or a signal post is equal to the time taken by the train to cover/metres.
Time taken by a train of length/metres to pass a stationery object of length b metres is the time taken by the train to cover (l + b) metres.
Suppose two trains or two objects bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed is = (u - v) m/s.
Suppose two trains or two objects bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s.
If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then: The time taken by the trains to cross each other = (a+b)/(u+v) sec
If two trains of length a metres and b metres are moving in the same direction at u m/s and v m/s, then: The time taken by the faster train to cross the slower train = (a+b)/(u-v) sec
If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then: (A's speed) : (B's speed) = (√b:√a)

Points to remember when solving train problem questions

Conversion Tables

Term	Symbol
Meter	m
Second	s
Hour	hr
Kilometer	km
Kilometer	per hour km/hr or kmph

Term	Meaning
1 hour	60 minutes
1 minute	60 seconds
1 hour	3600 seconds
1 kilometer	1000 meters
Kilometer per hour	Km/hr or kmph

Speed in Km/hr	Speed in m/s
18	5
36	10
54	15
72	20
90	25

Speed in m/s	Speed in Km/hr
1	3.6
2	7.2
5	18
10	36
20	72

Conversion formulae: Km/hr -> m/s [ Multiply by 5/18] m/s -> Km/hr [ Multiply by 18/5 or Multiply by 3.6]

Relative speed if trains moving in same direction
Relative speed of trains in opposite direction
When two trains are moving in the same direction, the distance covered is equal to the sum of the lengths of both trains.
Distance travelled when a train crosses a stationary object
Distance travelled when a train crosses a platform/bridge

Now let us first understand the different types of problems before we can solve a specific problem.

Type 1: Pole, Tree, Man standing [Stationary]

Suppose you visit the beach and remove one bucket of water from it. How much water has been reduced from the sea? The amount is almost insignificant, right?

Similarly, let's imagine that you're driving a train. If you need to overtake a person standing or pass by a tree, how long would the person or tree appear in comparison to the length of your train? Is it not negligible when compared to the train's size?

From this, we can conclude that the distance covered by the train to overtake a person, tree, or pole is equal to the length of the train.

Problem 1:

A train 100 m long is running at speed of 30km/hr. Find the time taken by it to pass man standing near the railway station.

Solution

Train length = 100 m

Speed of Train= 30 km/hr = 30

Time To pass Man standing = ?

As we know in order to pass man, train has to cover distance as her length

Time = Distance/Speed

Time = 100 / (25/3) = 100*3 /25 = 300/ 25 = 60 / 5 = 12

Answer is Time taken by Train to pass man standing near railway station is 12 seconds

Problem 2:

In what time will train 100 meters long cross an electric pole if its speed be 144 km/hr?

Solution

Train length = 100 m Speed of Train= 30 km/hr = 144*(5/18) = 8*5= 40 m/s.

Time To pass Man standing = ? As we know in order to pass electric pole, train has to cover distance as her length Time = Distance/Speed = 100/40 = 50/20 = 5/2 = 2.5 = 2.5 Answer is Time taken by Train to cross electric pole is 2.5 seconds.

Problem 3:

A train 280 m long running with speed of 63 km/hr will pass tree in?

Solution

Train length = 280 m

Speed of Train= 63 km/hr

= 63*(5/18) = 7*(5/2) = 35/2 m

= Time To pass Tree = ?

As we know in order to pass tree, train has to cover distance as her length

Time = Distance/Speed Time = 280/(35/2) = 80/5 = 16

Answer is Time taken by Train to pass tree is 16 seconds

Problem 4:

A train 132 m long passes electric pole in 6 seconds. Find the speed of train in km/hr.

Solution

Train length = 132 m

Time to cross pole = 6 seconds

Speed of Train= ?

As we know in order to pass electric pole, train has to cover distance as her length

And this distance is travelled by Train in 6 seconds

Speed = Distance/time

Speed = 132/6

Speed = 22 m/s

= 22*18/5 = 79.2km/hr

Answer is Speed of Train is 79.2 km/hr

Type 2: Bridge Platform

Lets consider another real-time scenario. Think of yourself as a train driver in Kolkata who is currently crossing the Howrah Bridge. Is it correct to say that the bridge's length is negligible in comparison to the train's length?

Absolutely not. If the train is 500 metres long, the bridge might be 200 metres long, 800 metres long, or even look like a platform or tunnel that is 1 or 2 km long. Wait until the last carriage of the train crosses the end of the platform to be sure you have completely passed the platform or bridge.

So in these problems:

Distance covered by train to pass bridge or platform = Length of Train + Length of platform

Problem 1:

A train moving at a speed of 132 km/hr. If length of the train is 110 meters, how long it will take to cross a railway platform 165 m long?

Solution

Speed of Train = 132 km/hr

= 132*(5/18)

= 110/3 m/s

Length of Train = 110 m

Railway platform length = 165m

In order to cross railway platform Train has to cover its distance + Length of Platform

Distance to cover = 110 m + 165 m = 275 m

Time = Distance / speed

= 275/ (110/3) = 15/2 = 7.5 seconds

Answer is Train will cross platform of 165m length in 7.5 seconds

Problem 2:

How long does a train 110 meters long running at speed of 72 km/hr take to cross a bridge of 132 meters in length?

Solution

Speed of Train = 72 km/hr

= 72*5/18 = 4*5 = 20m/s

Length of Train = 110 m

Bridge length = 132m

In order to Bridge Train has to cover its distance + Length of Bridge

Distance to cover = 110 m + 132 m = 242 m

Time = Distance / Speed

Time = 240/20 = 121/10 = 12.1

Answer is Train will cross Bridge of 132 m length in 12.1 seconds

Problem 3:

A goods train running at speed of 72 km/hr and crosses 250 m long platform in 26 seconds. What is length of goods train?

Solution

Speed of Train = 72 km/hr

= 72*5/18 = 4*5 = 20m/s

Platform length = 250 m and it is crossed by Goods Train in 26 seconds

Length of Train = ?

In order to cross platform Train has to cover its length + Length of Platform

Let us assume Train length as x meters

Distance covered = x + 250

X + 250 meters distance covered in 26 seconds.

As Train speed is 20 m/s :

In 26 seconds it will cover Distance = Speed * Time

= 20 * 26 = 520 m

We know that distance covered in 26 seconds is x + 250

So x + 250 = 520

x = 520 – 250 = 270 m

Answer is Length of Goods Train is 270 m

Problem 4:

A train 800 meters long running at speed of 78 km/hr. If it crosses a tunnel in 1 minute then length of tunnel in meters is?

Solution

Speed of Train = 78 km/hr

= 78* 5/18 = 13*5/3 = 65/3 m/s

= Length of Train = 800 m

Crosses Tunnel in 1 minute [60 seconds]

In order to cross Tunnel, Train has to cover its length + Length of Tunnel Let us assume Tunnel length as x meters

Distance covered = 800 + x

800 + x meters distance covered in 60 seconds.

As Train speed is 65/3 m/s

In 60 seconds it will cover Distance = Speed * Time

= (65/3)*60

= 65*20

= 1300

We know that distance covered in 60 seconds is 800 + x

So 800 + x = 1300

x = 1300 – 800 = 500 m

Answer is Length of Tunnel is 500 m

Relative Speed Concept:

Have you ever experienced the situation where you're sitting in a train and observing another train either moving in the same direction or coming from the opposite direction? If so, you may have noticed that the train coming from the opposite direction appears to be moving faster than our own train when viewed from the window. Similarly, when you observe a train moving in the same direction as yours, it may seem slower even if its actual speed is greater. This phenomenon can be attributed to the concept of relative speed. When two trains travel in opposite directions, they pass each other quickly, whereas when they travel in the same direction, the passing occurs at a slower pace.

When Train traveling from opposite direction,

Relative speed = Speed of Train1 + Speed of Train2

When both Trains are travelling in same direction,

Relative speed = Difference of 2 Trains speeds

If Speed of Train2 > Speed of Train1 then -> Speed of Train2 – Speed of Train1

If Speed of Train1 > Speed of Train2 then -> Speed of Train1 – Speed of Train2

Type 3: 2 Trains same direction

Problem 1:

Two trains 100 meters and 120 meters long are running in the same direction with speed of 72km/hr and 54 km/hr. In how much time 1st train will cross second?