# 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 two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 kmph. Then find the speed of faster train  ?

 A) 68 kmph B) 52 kmph C) 76 kmph D) 50 kmph

Explanation:

Let the speed of the faster train be 'X' kmph,
Then their relative speed= X - 48 kmph
To cross slower train by faster train,
Distance need to be cover = (400 + 600)m = 1 km. and
Time required = 180 sec = 180/3600 hr = 1/20 hr.
Time = Distance/Speed
=> 1/20 = 1/(x-48)
X = 68 kmph

15 14075
Q:

A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train ?

 A) 230 m B) 240 m C) 260 m D) 320 m

Explanation:

Relative speed = (120 + 80) km/hr

=(200*5/18)m/s = (500/9)m/s

Let the length of the other train be x metres.

Then, x+270/9 = 500/9

=>  x + 270 = 500

=>  x = 230.

18 13459
Q:

Two goods trains each 520 m long, are running in opposite directions on parallel tracks. Their speeds are 42 km/hr and 36 km/hr respectively. Find the time taken by the slower train to cross the driver of the faster one ?

 A) 60 sec B) 48 sec C) 45 sec D) 34 sec

Explanation:

Relative speed = 42 + 36 = 78 km/hr = $653$ m/s

Distance = (520 + 520) =1040 mts.

Time = $1040×365$= 48 sec

10 13341
Q:

Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is ?

 A) 387 kms B) 242 kms C) 145 kms D) 444 kms

Explanation:

1h ----- 5 kms
? ------ 60 kms

Time = 12 hrs

Relative Speed = 16 + 21 = 37 kmph

T = 12 hrs

D = S x T = 37 x 12 = 444 kms.

13 12251
Q:

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 : 2 B) 3 : 1 C) 4 : 7 D) 3 : 2

Explanation:

Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, length of the first train = 27 x meters, and

length of the second train = 17 y meters.

(27 x + 17 y) / (x + y) = 23

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

=> 4 x = 6 y

=> x/y = 3/2.

13 11908
Q:

How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction ?

 A) 58 sec B) 62 sec C) 60 sec D) 50 sec

Explanation:

The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.

Relative speed = 72 -36 = 36 kmph = 36 x 5/18 = 10 mps.

Time required = d/s = 500/10 = 50 sec.

8 11852
Q:

A train sets off at 3 p.m. at the speed of 70 kmph. Another train starts at 4:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet ?

 A) 10:10 pm B) 9:50 pm C) 11:30 pm D) 10:30 pm

Explanation:

Distance = 70 x 1 ½ = 105 km

Relative Speed = 85 – 70 = 15

Time = 105/15 = 7 hrs

4:30 + 7 hrs = 11.30 p.m.

17 11832
Q:

Train K crosses a stationary Train L in 50 seconds and a pole in 20 seconds with the same speed. The length of the Train K is 240 meters. What is the length of stationary Train L ?

 A) 60 mts B) 120 mts C) 240 mts D) 360 mts