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 stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?

A) 10.30 B) 10
C) 8.45 D) 9.30
 
Answer & Explanation Answer: B) 10

Explanation:

Assume both trains meet after x hours after 7 am

Distance covered by train starting from P in x hours = 20x km

Distance covered by train starting from Q in (x-1) hours = 25(x-1)

Total distance = 110

=> 20x + 25(x-1) = 110

=> 45x = 135

=> x= 3

Means, they meet after 3 hours after 7 am, ie, they meet at 10 am

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38 26100
Q:

A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is:

A) 50 m B) 150 m
C) 200 m D) data inadequate
 
Answer & Explanation Answer: B) 150 m

Explanation:

Let the length of the train be x metres and its speed be y m/sec.
Then, (x/y)= 15   y =(x/15)

 

(x+100)/25 = x/15

 

=> 15(x + 100) = 25x

 

=> 15x + 1500 = 25x

 

=> 1500 = 10x

 

=> x = 150 m.

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39 23275
Q:

Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time (in seconds) which they take to cross each other, is:

A) 9 B) 9.6
C) 10 D) 10.8
 
Answer & Explanation Answer: D) 10.8

Explanation:

Relative speed = (60 + 40) km/hr =[ 100 x ( 5 / 18 ) ]m/sec = ( 250 /9 ) m/sec.
Distance covered in crossing each other = (140 + 160) m = 300 m.
Required time = [ 300 x ( 9/250 ) ] sec = ( 54/ 5 )sec = 10.8 sec.

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24 22382
Q:

A train moves with a speed of 108 kmph. Its speed in metres per second is :

A) 10.8 B) 18
C) 30 D) 38.8
 
Answer & Explanation Answer: C) 30

Explanation:

108 kmph = 108*[5/18] m/sec = 30 m / s.

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42 21144
Q:

Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?

A) 48 B) 24
C) 38 D) 36
 
Answer & Explanation Answer: B) 24

Explanation:

Less Cogs  more turns and less time  less turns

 

    Cogs  Time  TurnsA  54       45       80B   32       8          ?

Number of turns required=80 × 54/32 × 8/45  = 24 times

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57 19633
Q:

A train 110 metres long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

A) 5 B) 6
C) 7 D) 10
 
Answer & Explanation Answer: B) 6

Explanation:

Speed of train relative to man = (60 + 6) km/hr = 66 km/hr.

[66*(5/18)] m/sec = (55/3) m/sec

Time taken to pass the man = [110*(3/55)]m/sec = 6 sec.

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13 19173
Q:

A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train ?

A) 69.5 km/hr B) 70 km/hr
C) 79 km/hr D) 79.2 km/hr
 
Answer & Explanation Answer: D) 79.2 km/hr

Explanation:

Let the length of the train be x metres and its speed by y m/sec.


Then, x/y = 8 => x = 8y


Now, (x+264)/20 = y
8y + 264 = 20y
y = 22.
Speed = 22 m/sec = (22*18/5) km/hr = 79.2 km/hr.

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57 15874
Q:

Two trains having equal lengths, take 10 seconds and 15 seconds respectively to cross a post. If the length of each train is 120 meters, in what time (in seconds) will they cross each other when traveling in opposite direction?

A) 10 B) 25
C) 12 D) 20
 
Answer & Explanation Answer: C) 12

Explanation:

Speed of train 1 = 12010m/sec = 12 m/sec 

Speed of train 2 =12015m/sec  = 8 m/sec 

if they travel in opposite direction, relative speed = 12 + 8 = 20 m/sec

distance covered = 120 + 120 = 240 m

time = distance/speed = 240/20 = 12 sec

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22 15391