# 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:

The distance between the two railway stations is 1176 km. To cover this distance, an express train takes 5 hours less than a passenger train while the average speed of the passenger train is 70 km/h less than that of the express train. The time taken by the passenger train to complete the travel is:

 A) 12 hours B) 23 hours C) 17 hours D) 18 hours

Explanation:

3 674
Q:

A train without stop page travels with an average speed of 65 km/h and with stop page,it travels with an average speed of 52 km/h. For how many minutes does the train stop on an average per hour?

 A) 14 B) 13 C) 12 D) 15

Explanation:

1 661
Q:

A train without stop page travels with an average speed of 70km/h, and with stoppage, it travels with the average speed of 56km/h. How many minutes, does the train stop on an average per hour?

 A) 12 B) 14 C) 16 D) 15

Explanation:

3 660
Q:

A train without stoppage travels with an average speed of 50 km/h, and with stoppage, it travels with an average speed of 40 km/h. For how many minutes does the train stop on an average per hour ?

 A) 12 B) 13 C) 14 D) 15

Explanation:

1 600
Q:

A train travels the distance between stations P and Q at a speed of 126 km/h, while in the opposite direction it comes back at 90 km/h. Another train travels the same distance at the average speed of the first train. The time taken by the second train to travel 525 km is:

 A) 4 hours 20 min B) 5 hours 20 min C) 5 hours D) 4 hours

Explanation:

2 588
Q:

A train, 150 m long is running at 90 km/h. How long (in seconds) will it take to clear a platform that is 300 m long?

 A) 6 B) 12 C) 50 D) 18

Explanation:

1 540
Q:

Train ‘A’ runs at a speed of 80 kmph and leaves station ‘X’ at 11.00 a.m. Train ‘B’ leaves station ‘X’ at 11.15 a.m.in the same direction, on the same day . At what speed train ‘B’ should run in order to catch train ‘A’ at station ‘Y’ located at a distance of 60 km?

 A) 120 km/h B) 125 km/h C) 115 km/h D) 110 km/h

Explanation:

4 533
Q:

A train without stoppage travels with an average speed of 80 km/h and with stop page, it travels with an average speed of 72 km/h. For how many minutes does the train stop on an average per hour?

 A) 6 B) 8 C) 9 D) 7