# 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:

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

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.

32 32420
Q:

A train travelling at a speed of 75 mph enters a tunnel $312$miles long. The train is $14$mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?

 A) 2.5 min B) 3 min C) 3.2 min D) 3.5 min

Explanation:

Total distance covered =$72+14$miles =$154$miles

Time taken = $154*75$hrs = $120$ hrs =$120*60min$ = 3 min

50 30298
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

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.

40 27694
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

Explanation:

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

(x+100)/25 = x/15

=> 15(x + 100) = 25x

=> 15x + 1500 = 25x

=> 1500 = 10x

=> x = 150 m.

54 26350
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

Explanation:

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

55 25220
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

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.

16 22736
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

Explanation:

Less Cogs $\inline \fn_jvn \Rightarrow$ more turns and less time $\inline \fn_jvn \Rightarrow$ less turns

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

62 21323
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

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.