# 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 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
$\inline \fn_jvn \Rightarrow$8y + 264 = 20y
$\inline \fn_jvn \Rightarrow$y = 22.
$\inline \fn_jvn \therefore$Speed = 22 m/sec = (22*18/5) km/hr = 79.2 km/hr.

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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

33 17774
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.

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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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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 = $distancetime$m/s

$⇒352=170+x30$

-->  x = 355 mts.

27 16822
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

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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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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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= 100 mts.