Quantitative aptitude questions on trains are a special case of time and distance problems. In this article, you will learn the concepts related to an important topic in Time, Speed and Distance i.e. Trains.

**Formula's For Problems On Trains**

1. Time taken by a train of length X meters to pass a pole or standing man or a signal post is =** the time taken by the train to cover X meters. **

2. Time taken by a train of length X meters to pass a stationary object of length b meters is = **the time taken by the train to cover (X+ b) meters. **

3. 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. **

4. 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. **

5. If two trains of length a meters and b meters are moving in opposite directions at um/s and v m/s, then:

**The time taken by the trains to cross each other = (a + b) / (u + v) sec**

6. If two trains of length a meters and b meters are moving in the same direction **at um/**s and v m/s, then:

**The time taken by the faster train to cross the slower train = (a + b) / (u - v) sec**

7. 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 ) **

**Problems On Trains**

### 1) A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?

A) 200 metres

B) 160 metres

C) 190 metres

D) 120 metres

### 2) A train, 130 metres long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is

A) 235 metres

B) 245 metres

C) 270 metres

D) 220 metres

### 3) A train has a length of 150 metres. It is passing a man who is moving at 2 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.

A) 152 km/hr

B) 169 km/hr

C) 182 km/hr

D) 180 km/hr

### 4) A train having a length of 240 metre passes a post in 24 seconds. How long will it take to pass a platform having a length of 650 metre?

A) 99 seconds

B) 89 seconds

C) 120 seconds

D) 80 seconds

**Q5) Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:**

A) 1 : 3

B) 3 : 2

C) 3 : 4

D) None of these

**Solution :**

*x*m/sec and y m/sec respectively.

Then, length of the first train = 27

*x*metres,

and length of the second train = 17

*y*metres.

27x + 17y / x + y = 23

=> 27x + 17 y = 23x + 23y

=> 4x =6y

x/ y = 3/2

**Q6) Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:**

A) 50 m

B) 72 m

C) 80 m

D) 82 m

**Solution :**

*x*metres.

Then, distance covered = 2

*x*metres.

Relative speed = (46 - 36) km/hr

= 10(5/18) m/sec

= 25/9 m/sec

= 2x / 36 = 25/9

2x =100

= x = 50 m

**Q7) A train travelling at 60 kmph crosses another train travelling in the same direction at 50 kmph in 30 seconds. What is the combined length of both the trains?**

A) 250/3 metres

B) 250/7 metres

C) 255/3 metres

D) None

**Solution :**

Speed of train B = = 50 kmph = 50 *(5/18) = 125/9 m/sec

The relative speed =(50/3)-(125/9)=25/9 m/s (we have subtracted the two values because both the trains are going in the same direction)

Time taken by train A to cross train B = 30 secs

Distance = Speed * Time

Distance =25/9 * 30 = 250/3 metres (i.e. the combined length of both trains)

**Q8) Two trains start at the same time from Pune and Delhi and proceed towards each other at 80 kmph and 95 kmph respectively. When they meet, it is found that one train has travelled 180 km more than the other. Find the distance between Delhi and Pune.**

A) 1200 kms

B) 2120 kms

C) 2000 kms

D) 2100 kms

**Solution :**

Distance

_{1}= Speed * Time = 80 * t = 80t

Distance

_{2}= Speed * Time = 95 * t = 95t

As the distance gap between both trains is 180 kms

Therefore, we can say that:

95t - 80t = 180

15t = 180

t = 12 seconds

Total Distance, (95+80) t = 175 * 12 (t = 12)

Distance = 2100 kms

**Q9) Indrayani Express leaves Pune for Bombay at 17:30 hrs and reaches Bombay at 21:30 hrs. While, Shatabdi, which leaves Bombay at 17:00 hrs reaches Pune at 20:30 hrs. At what time do they pass each other?**

A) 19:06 hrs

B) 18:00 hrs

C) 19:16 hrs

D) None

**Solution :**

Indrayani’s Speed =(d/4) kmph and that of Shatabdi = (d/3.5)kmph

Let t be the time in hrs after Shatabdi has left for Pune, when the two trains meet

Therefore, distance travelled by Shatabdi = (d/3.5)* t

And that of Indrayani =(d/4) * (t-30/60)

The sum of the distances travelled by the two trains = distance between Bombay and Pune = d km

Therefore, (d/3.5)* t +(d/4) * (t-30/60)=d

Solving for t, we get t = 2.1 hrs or 2 hrs and 6 mins

Hence, the two trains meet at 19:06 hrs

**Q10) A train of length 240 meters crosses a pole in 12 seconds. In what time it will cross a platform of length 400 meters?**

A) 33 seconds

B) 35 seconds

C) 37 seconds

D) 39 seconds

**Solution :**

Distance covered = length of train + length of platform

= 240 + 400 = 660 meters

Speed of train = Distance (length of train) / time taken to cross the pole

So,time taken to cross the platform =