Tricks to solve Problems on Trains

Problems on trains are very common in competitive exams. Various types of questions are asked on trains. Questions on trains are solved using the concept of time, speed and distance i.e. we use the formulas of time, speed and distance to solve questions on trains.

  • Speed=Distance/Time
  • If Time is constant,SpeedDistance
  • If Distance is constant,Speed1/Time
  • If Speed is constant,DistanceTime
  • km/hr to m/s conversion:
    a km/hr = a x 5 m/s.
    18
  • m/s to km/hr conversion:
    a m/s = a x 18 km/hr.
    5
  • Time taken by a train of length l meters to pass a pole or standing man or a signal post is equal to the time taken by the train to cover l meters.
  • Time taken by a train of length l meters to pass a stationery object of length b meters is the time taken by the train to cover (l + b) meters.
  • 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.
  • 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.
  • If two trains of length a meters and b meters are moving in opposite directions at u m/s and v m/s, then:
    The time taken by the trains to cross each other = (a + b) sec.
    (u + v)
  • If two trains of length a meters and b meters are moving in the same direction at u m/s and v m/s, then:
    The time taken by the faster train to cross the slower train = (a + b) sec.
    (u – v)

 

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 – General Examples

 

1) A train moving at speed of 80 km/hr crosses a pole in 7 seconds. Find the length of the train.

  1. 150 m
  2. 165 m
  3. 175 m
  4. 170 m

The correct option is (C).

Answer with explanation:

Length of the train is equal to the distance covered by train to cross the pole. So, we will find the distance travelled by the train in 7 seconds by applying the following formula:

Distance= Speed x Time

Speed is given in Km/hr so we will convert it into m/s as answers are given in meters.

Speed=90* Apti Problem on trains 8= 25 m/s

Time = 7 seconds

Distance = 25 * 7= 175 meters

2) A train of length 200 meters crosses a man running at 10 km/hr in the same direction in 10 seconds. What is the speed of the train?

  1. 72 km/hr
  2. 95 km/hr
  3. 85 km/hr
  4. 82 km/hr

 The correct option is (D).

Answer with explanation:

When the train and man are moving in same direction then relative speed will be the difference between their individual speeds. In this problem the other way to find the relative speed is to divide the distance covered (length of train) by the time taken by the train to cross the man.

Relative Speed=Apti Problem on trains 9

We will convert it into Km/hr

Apti Problem on trains 10= 72 km/hr

Now, let the speed of the train is X km/hr. So, the relative speed, 72 km/hr = X km/hr ? 10 km/hr

X-10=72

X= 72+10

X= 82 km/hr

3)

A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A. 120 m
B. 240 m
C. 300 m
D. None of these

The correct Option is B

Answer with Explanation:

Speed = 54 x 5 m/sec = 15 m/sec.
18

Length of the train = (15 x 20)m = 300 m.

Let the length of the platform be x metres.

Then, x + 300 = 15
36

 x + 300 = 540

 x = 240 m.

 

 

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is

A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?

Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:

Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?

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