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.
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 |
ğŸ’¡Distance = Speed * Time
ğŸ’¡Speed = Distance/Time
ğŸ’¡Time = Distance/Speed
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]
Now let us first understand the different types of problems before we can solve a specific problem.
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.
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?
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?
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.
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
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?
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?
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?
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 â€“ 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?
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 â€“ 800 = 500 m
Answer is Length of Tunnel is 500 m
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 â€“ Speed of Train1
If Speed of Train1 > Speed of Train2 then -> Speed of Train1 â€“ Speed of Train2
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?
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