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 = (a+b)(u+v)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 = a+bu-vsec.

 

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) = b:a

Q:

Two trains are moving in opposite directions at 60 km/hr and 90 km/hr. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is ?

A) 42 sec B) 44 sec
C) 46 sec D) 48 sec
 
Answer & Explanation Answer: D) 48 sec

Explanation:

Relative speed = 60 + 90 = 150 km/hr.

= 150 x 5/18 = 125/3 m/sec.

Distance covered = 1.10 + 0.9 = 2 km = 2000 m.

Required time = 2000 x 3/125 = 48 sec.

Report Error

View Answer Report Error Discuss

8 14505
Q:

Two trains of equal length , running in opposite directions , pass a pole in 18 and 12 seconds. The trains will cross each other in 

A) 14.4 sec B) 15.5 sec
C) 18.8 sec D) 20.2 sec
 
Answer & Explanation Answer: A) 14.4 sec

Explanation:

Let the length of the train be L metres

 

Speed of first train = 360018xL m/hour

 

Speed of secxond train = 360012xL m/hour

 

When running in opposite directions, relative speed = 200 L + 300 L m/hour

 

Distance to be covered = L + L = 2L metre

 

Time taken = 2L500Lx3600 sec

 

                 =14.4 sec

Report Error

View Answer Report Error Discuss

25 13949
Q:

Length of train is 170 meters and speed of train is 63 km/hour. This train can pass a bridge in 30 seconds, then find the length of the bridge.

A) 355 mts B) 325 mts
C) 365 mts D) 312 mts
 
Answer & Explanation Answer: A) 355 mts

Explanation:

Given speed = 63 km/hr = 63×518=352 m/s

Let the length of the bridge = x mts

Given time taken to cover the distance of (170 + x)mts is 30 sec.

We know speed = distancetimem/s

352=170+x30

 -->  x = 355 mts.

Report Error

View Answer Report Error Discuss

18 13825
Q:

A train covers a distance between station A and station B in 45 min.If the speed of the train is reduced by 5 km/hr,then the same distance is covered in 48 min.what is the distance between the stations A and B ?

A) 80 kms B) 60 kms
C) 45 kms D) 32 kms
 
Answer & Explanation Answer: B) 60 kms

Explanation:

Let 'd' be the distance and 's' be the speed and 't' be the time
d=sxt
45 mins = 3/4 hr and 48 mins = 4/5 hr
As distance is same in both cases;
s(3/4) = (s-5)(4/5)
3s/4 = (4s-20)/5
15s = 16s-80
s = 80 km.
=> d = 80 x 3/4 = 60 kms.

Report Error

View Answer Report Error Discuss

18 13268
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
 
Answer & Explanation Answer: A) 230 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.

Report Error

View Answer Report Error Discuss

18 12779
Q:

Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions  ?

A) 10 sec B) 11 sec
C) 12 sec D) 8 sec
 
Answer & Explanation Answer: A) 10 sec

Explanation:

Relative Speed = 60 -40 = 20 x 5/18 = 100/18

Time = 50

Distance = 50 x 100/18 = 2500/9

Relative Speed = 60 + 40 = 100 x 5/18

Time = 2500/9 x 18/500 = 10 sec.

Report Error

View Answer Report Error Discuss

12 12777
Q:

A train running at the speed of 40 km/hr crosses a signal pole in 9 seconds. Find the length of the train ?

A) 90 mts B) 150 mts
C) 120 mts D) 100 mts
 
Answer & Explanation Answer: D) 100 mts

Explanation:

We know that   Speed=distancetime 

distance= speed * time


 d=40×518×9 

   d= 100 mts.

Report Error

View Answer Report Error Discuss

11 11986
Q:

Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a girl sitting at window seat in the slower train in 32 seconds. Find the length of the faster train ?

A) 170 m B) 100 m
C) 270 m D) 320 m
 
Answer & Explanation Answer: D) 320 m

Explanation:

Relative speed = (72 - 36) x 5/18 = 2 x 5 = 10 mps.
Distance covered in 32 sec = 32 x 10 = 320 m.

The length of the faster train = 320 m.

Report Error

View Answer Report Error Discuss

10 11142