# How to Easily Solve Problems on Trains and Find the Distance between Trains

### problems on trains

Problems on trains are there on the curriculum of every competitive exam like IBPS PO, SBI PO, SBI Clerk, IBPS Clerk, SSC CGL, SSC CHSL etc Exams. However, they can really confuse you because of the details you have to take into consideration and also the steps involved.
The 21st smart method in this series of blog posts will help you find the distance between trains in 5- 10 seconds that would otherwise take you 30- 45 seconds.

### Problems on Trains

A hot favourite, problems on trains are of many kinds be very confusing because it involves taking into account a lot of details like- directions, the length of the train, length of the station, the distance between trains, along with also remembering that both trains also have different speeds. And of course! You have to remember the list of formulas.

### Formulas to Solve Problems on Trains

1. Time taken by a train x mts long to pass an object of lengthy mts

2. If two trains are moving in opposite directions at v1 m/s and v2 m/s, then their relative speed

3. Assume two trains of length x mts and y mts are moving in opposite directions at v1 m/s and v2 m/s, then the time taken by the trains to cross each other

4. Assume two trains of length x mts and y mts are moving in the same direction at v1 m/s and v2 m/s where v1> v2, Then the time taken by the faster train to cross the slower train

### Example of Problems on Trains

Two trains start at the same time from A and B and proceed towards B and A at 36 kmph and 42 kmph respectively. When they meet, it is found that one train has moved 48 km more than the other. What is the distance between trains, A and B?
1) 624 km      2) 636 km      3) 544 km      4) 460 km      5) None of these

### Conventional Method to Solve Problems on Trains

The usual approach starts with assuming the distance between the two trains A and B to be ‘D’
Then we assume the distance of the meeting point ‘Y’ from A
Step 1:
x+ 48 => x+(x+48) = d
Since the two trains start at the same time, the time taken by each train to reach the meeting point is equal.
Step 2:
T1 = T2
Step 3:
D1/S1 = D2/S2 (since t = d/s)
Step 4:
Y/36 = (Y+48)/42
Step 5:
7Y = 6Y+288
Step 6:
Y = 288
Step 7:
D= Y+(Y+48)
Step 8:
D = 288+288+48 = 624 km
The above method is 100% accurate though we definitely can’t say the same about the speed of the method.

### Smart Method to Solve Problems on Trains

Speed with accuracy is what matters in a competitive exam and using the long method is not a good idea.
Distance covered by first train in 1 hour is 36 km and that covered by the second train is 42 km

Step 1:
Difference of distances covered by the two trains in 1 hour = 42 – 36 = 6km
Therefore the relative speed is 6km

Step 2:
The difference between the distance covered by the two trains for the meeting point = 48 km

Step 3:
Therefore the time for which the two trains have travelled = 48/6 = 8 hours

Step 4:
Distance covered by the two trains together in 1 hour = 36 km+42km=78 km

Step 5:
Required answer = 78×8 = 624 km
By using the simple concept of proportionality equations we filter out excess calculation and save valuable time.
Solve the following problems on trains and find the distance between trains-
Question 1: A train leaves station A at the speed of 30 kmph. At the same time, another train departs from station B at the speed of 45 kmph. When they meet, it is found that one train has travelled 60 km more than the other. What is the distance between trains, A and B?
1) 150 km      2) 300 km      3) 360 km      4) 240 km      5) None of these
Question 2: Two trains start at the same time from A and B and proceed towards B and A at 38km/h and 46 km/h respectively. When they meet, it is found that one train has moved 64km more than the other. What is the distance between trains, A and B?
1) 672 km      2) 636 km      3) 544 km      4) 460 km      5) None of these
Write your answers in the comments below and tell us how long it took you to find the distance between the trains!
Keep watching this space for more smart methods and remember to use these smart methods when you practice!