# Problems on Trains

09 May 2023

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

A) 200 metres

B) 160 metres

C) 190 metres

D) 120 metres

A) 235 metres

B) 245 metres

C) 270 metres

D)  220 metres

A) 152 km/hr

B) 169 km/hr

C) 182 km/hr

D) 180 km/hr

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 :

Let the speeds of the two trains be x m/sec and y m/sec respectively.
Then, length of the first train = 27x metres,
and length of the second train = 17y 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 :

Let the length of each train be x metres.
Then, distance covered = 2x 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 A = 60 kmph = 60* (5/18) = 50/3 m/sec
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 :

Let t be the time after they meet
Distance1 = Speed * Time = 80 * t = 80t
Distance2 = 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 :

Let the distance between Bombay and Pune = d km
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 :

Time taken to cross the platform = 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 = 