# Problems on Trains Questions

FACTS  AND  FORMULAE  FOR  PROBLEMS  ON  TRAINS

1. a km/hr = [a x (5/18)] m/s.

2. a m/s = [a x (18/5)] km/hr.

3. Time taken by a train of length l metres to pass a pole or a standing man or a signal post is equal to the time taken by the train to cover l metres.

4. Time taken by a train of length 1 metres to pass a stationary object of length b metres is the time taken by the train to cover (1 + b) metres.

5. Suppose two trains or two bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relatives speed = (u - v) m/s.

6. Suppose two trains or two bodies are moving in opposite directions at u m/s and v m/s, then their relative speed = (u + v) m/s.

7. If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then time taken by the trains to cross each other = $\frac{\left(a+b\right)}{\left(u+v\right)}$sec.

8. If two trains of length a metres and b metres 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 = $\frac{\left(a+b\right)}{\left(u-v\right)}$sec.

9. 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) = $\left(\sqrt{b}:\sqrt{a}\right)$

Q:

Two trains are moving in opposite directions with the same speed. If the length of each train is 144 metres and they cross each other in 9 seconds, then what is the speed (in km/hr) of each train?

 A) 53 B) 57.6 C) 60.4 D) 64.8

Explanation:

1 1012
Q:

Two trains are moving towards each other with the speed of 25 km/hr and 83 km/hr respectively. What will be the distance (in metres) between the trains  one second before collide?

 A) 32 B) 35 C) 30 D) 40

Explanation:

1 990
Q:

Train X travelling at 60 km/h overtakes another train Y, 225 m long, and completely passes it in 72 seconds. If the trains had been going in opposite directions, they would have passed each other in 18 seconds. The length (in m) of X and the speed (in km/h) of Y are, respectively:

 A) 245 and 54 B) 255 and 40 C) 255 and 36 D) 245 and 45

Explanation:

0 967
Q:

A train travelling at constant speed crosses two persons walking in the same direction in 8 seconds and 8.4 seconds respectively. The first person was walking at the speed of 4.5 km/hr while the second was walking at the speed of 6 km/hr. What was the speed of the train in km/hr?

 A) 42 B) 40 C) 32 D) 36

Explanation:

0 942
Q:

Two trains, one 153 m long and the other 127 m long; coming from opposite directions crossed each other in 7.2 seconds. The combined speed of the two trains every hour would then be:

 A) 140 km/h B) 105 km/h C) 70 km/h D) 280 km/h

Explanation:

0 927
Q:

A 160 m long train crosses a 740 m long bridge in 40.5 seconds. What is the speed of the train?

 A) 80 kmph B) 85 kmph C) 75 kmph D) 70 kmph

Explanation:

1 915
Q:

Two trains, one 150 m long and the other 130m long, coming from opposite directions crosssed each other in 7.2 seconds. The sum of speed of the two trains every hour would then be

 A) 280 km B) 105 km C) 70 km D) 140 km

Explanation:

2 893
Q:

Two trains are moving in the same direction at the speed of 23 km/hr and 77 km/hr. The time taken by faster train to cross a man sitting in the slower train is 40 seconds. What will be the length (in metres) of the faster train?

 A) 720 B) 640 C) 600 D) 540