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 Problems on Trains Questions

Popular Latest Rated Important Formulae

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 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.

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11 12687
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
 
Answer & Explanation Answer: B) 48 sec

Explanation:

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

Distance = (520 + 520) =1040 mts.

Time = 1040×365= 48 sec

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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
 
Answer & Explanation Answer: 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.

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11 11398
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
 
Answer & Explanation Answer: A) 68 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

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14 10969
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
 
Answer & Explanation Answer: 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.

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11 10606
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
 
Answer & Explanation Answer: D) 360 mts

Explanation:

Speed of the Train K is given by s = d/t = 240/20 = 12 m/s
Distance covered by Train K in 50 seconds = 12 x 50 = 600 mts.
But it crosses Train L in 50 seconds
Therefore, the length of the Train L is = 600 - 240 = 360 mts.

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Q:

A train for Fathehpur leaves for every 2 hrs 30 min from Agra station. An announcement was made that train left 37 mins ago and next train comes at 17:00hrs. At what time was the announcement made ? 

A) 15:07 hrs B) 15:20 hrs
C) 15:05 hrs D) 15:00 hrs
 
Answer & Explanation Answer: A) 15:07 hrs

Explanation:

Next train comes at 17:00 hrs.
So, last train will be = 17:00hrs - 2:30hrs
= 14:30hrs
Announcement made after 37 min of the last train.
S0, 14:30hrs + 00:37 min
= 15:07 hrs.

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Q:

Two trains are running at 60 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 6 seconds. What is the length of the fast train ?

A. 6623 mts

B. 6632 mts

C.6345 mts

D. 6354 mts

A) Option A B) Option B
C) Option C D) Option D
 
Answer & Explanation Answer: A) Option A

Explanation:

As Trains are moving in same direction,

Relative Speed = 60-20 = 40 kmph

--> 40×518=1009 m/sec

 

Length of Train= Speed * Time

 

Length = 1009×6

⇒2003=6623 mts 

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