Hi, Welcome back to learn aptitude. Today we are going to look take a look on Problems on Trains. As you can see in any aptitude examination, you can find at least one Train based problem. In this post you will get various basic Problems on Trains. So lt’s get started.

### 1. Unit Conversion Formula

Conversion is a simple problem that you may face in the every Train based problems. The conversion problems are to convert **Km/Hour to Meter/Sec or Meter/Sec to Km/Hour.**

So when the question is to convert KM/Hour to Meter/Second then we have to multiply by ^{5}⁄_{18 , }and when the question asking to convert meter/sec to Km/Hour then multiply by ^{18}⁄_{5 .}

**‘A’ Km/Hour = A ×**^{5}⁄_{18 }M/Sec**‘B’ m/Sec = B ×**_{ }**.**^{18}⁄_{5 }Km/Hour

**Q.1 Convert 54 Km/Hr to M/Sec?**

**Solution: **54Km/Hour= 54 × ^{5}⁄_{18 } =15 m/Sec

**Q.2 Convert 50 m/Sec to Km/Hr?**

**Solution: **50 m/Sec= 50 × ^{18}⁄_{5 } =180 Km/Hr

### 2. Time and Distance Formula

The most important formula to solve Problems on Trains is Time and Distance formula. So just Remember this formula and your rest work is done.

Let Distance covered by the train =d

and the time take by the train = t

**Hence Speed of the Train ‘s’=**

**Q. A train is 500m long and its speed is 100m/Sec. Find the time taken by the train to cross a poll.**

Here S = 100

d= 500m/Sec

We know that s=

So t= ^{500}⁄_{100}=_{ }5 Sec

### Related Topic

### 3. Train with an object

In this type train has to cross an object like platform, Tunnel or Bridge etc. To solve this type of problem we have to use the following concept.

Let the length of the Train = L1, and the length of the Tunnel/Platform/ Bridge = L2 and time taken to cross the bridge = t and speed= s.

When the train completely, cross the object the total length = L1 + L2

Hence the Speed (S) =

**Q.3 A train is 200m long and is running at 72 Km/Hour. At what time it will pass 100mt long, bridge?**

(A) 20sec

(B) 30sec

(C) 40sec

(D) 50sec

**Answer: (A) 20sec**

**Solution: **L1= 300m

L2= 100m

S= 72 Km/Hr

T= (300+100)/20 = 20Sec

**Q.4 A train is 200m long and is running at 72 Km/Hour. At what time it will pass 100mt long, bridge?**

(A) 20sec

(B) 30sec

(C) 40sec

(D) 50sec

**Answer: (A) 20sec**

**Solution: **L1= 300m

L2= 100m

S= 72 Km/Hr

T= (300+100)/20 = 20Sec

**Q.5 A train 200m long is running at the speed 30Km/Hr. Find the time taken by the train to pass a poll near it?**

(A) 9sec

(B) 3sec

(C) 4sec

(D) 8sec

**Answer: (D) 8sec**

**Solution: **L1= 300m

L2= 100m

S= 72 Km/Hr

T= (300+100)/20 = 20Sec

## Theory of Relativity on Train Problems

There are two types of theory of relativity.

- Two Trains Moving Opposite to each other
- Two Trains Moving in the same Direction

### 4. Two Trains Crossing Each Other in Opposite Direction

Let’s assume two trains T1 and T2 of length L1 and L2 respectively. Two trains are moving in the opposite direction to each other.

Train T1’s speed is v1 and train T2’s speed is V2.

Here we have to calculate the time taken by the two train to cross each other completely.

In our case the two trains have to cross each other’s length i.e L1+L2 distance.

Let’s assume that you are travelling on a train with a speed of 80Km/Hr. You just see another train passing you at a speed of 30Km/Hr. You feel that the opposite train is moving faster than your train. While your train is moving at a faster speed. This is happening due to the addition of speed of both the train. You feel the speed of 70+30= 100Km/Hr.

Similarly in our case speed will be considered as V1+ V2

**∴ Time (t) = **

**Q. Two Trains A and moving to each other at a speed of 42Km/Hr and 48 Km/Hr to each other respectively. The length of train A is 137 meters and the length of train B is 163m. How many times they will take to cross each other?**

(A) 12.0 Sec

(B) 9.0Sec

(C) 7.2 Sec

(D) 6.3 Sec

**Answer: (A) 12.0 Sec**

**Solution: **L1= 137m

L2= 163m

V1 = 42 Km/Hr ,

V2 = 48 Km/Hr ,

V= V1+ V2 = 42+ 48= 90Km/Hr = 90 × 5/18= 25m/Sec

T= = 300/ 25= 12 Sec

**5. Two trains moving in the Same Direction**

Let’s assume train T1 and train T2 of length L1 and L2 are moving in the same direction at a speed of V1 and V2 respectively.

Here also the length will be = L1+ L2

Let’s assume you are travelling in a train at a speed of 50Km/Hr and you find another train is moving in the same direction at the same speed. You will feel that two trains are not moving. This is due to subtraction of speed.

Similarly, in our case the overall speed can be calculated by subtracting the both train’s speed.

Speed= V1 – V2

**∴ Time (t) = **

**Q. Two Trains A and moving in the same direction at a speed of 72Km/Hr and 54 Km/Hr to each other respectively. The length of train A is 100m and the length of train B is 120m. How many times they will take to cross each other?**

(A) 48 Sec

(B) 46 Sec

(C) 42 Sec

(D) 49 Sec

**Answer: (B) 46 Sec**

**Solution: **L1= 100m

L2= 120m

V1= 72 Km/Hr, V2= 54Km/Hr

As two trains moving in the same direction so Relative Speed of train V= V1- V2 = 72-54 = 18 Km/Hr= 18 × 5⁄18= 5 m/ Sec

T= (100+120)/5= 44 Sec

## Problems on Trains

**Q.1 A train is 150m long running on a train line at a speed of 68kmph. In what time it will cross a horse running at a speed of 8Km/Hr in the same direction?**

(A) 15 Sec

(B) 14 Sec

(C) 9 Sec

(D) 12 Sec

**Answer: (C) 9 Sec**

**Solution: **Speed of the train = 68 Km/Hr

Speed of horse= 8Km/Hr

Relative speed = 68- 8= 60=68 × (5/18) = (5/30)m/ Sec

Time taken by the Train to cross the Horse = = 9 Sec

**Q.2 A train is running at 54Km/Hr speed and it takes 20 Sec to pass a Tonnel. Next it takes 12 Second to pass a Woman walking at 6Km/Hr in the same direction in which train is running. Find ****the length of the Tunnel? **

(A) 140m

(B) 200m

(C) 220m

(D) 500m

This is one of the most important Problems in Trains section.

**Answer: (A) 140 m**

**Solution: **Relative speed of train with respective to the Woman= (54-6)Km/Hr = 48 Km/Hr= 48 × (5/18) = (40/3)m/Sec

When the train will pass the Woman, the train will cover its own length with Relative speed.

∴ Length of the train = Speed × Time = (40/3) × 12= 160m

Speed of Train = 54 Km/Hr = 54 × (5/18) = 15 m/Sec

When the train will cross the Tunnel, it will cover tunnel length along with its own length.

Let the Tunnel Length be x

Speed = (Tunnel Length + Train Length) / Time

⇒20 = (x+160)/ 15

⇒ x+ 160 = 20 × 15

⇒ x= 300 – 160

⇒ x = 140

∴ The length of the Tunnel = 140m