Problems On Trains

What is the length of a running train P crossing another running train Q?
I.	These two trains take 18 seconds to cross each other.
II.	These trains are running in opposite directions.
III.	The length of the train Q is 180 metres.

A:

I only

B:

II only

C:

III only

D:

All I, II and III are required

Answer: E

Let the length of the train P be x metres.

II. These trains are running in opposite directions.

III. Length of the train Q is 180 m.

I. Time taken by P to cross Q =	(180 + x)	18 =	(180 + x)
	Relative speed		Relative speed

Thus, even with I, II and III, the answer cannot be obtained.

Correct answer is (E).

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At what time will the train reach city X from city Y?
I.	The train crosses another train of equal length of 200 metres and running in opposite directions in 15 seconds.
II.	The train leaves city Y at 7.15 a.m. for city X situated at a distance of 558 km.
III.	The 200 metres long train crosses a signal pole in 10 seconds.

A:

I only

B:

II only

C:

III only

D:

II and III only

Answer: D

From the statement I, we get length of the train is 200 metres (Redundant info while comparing with Statement III). The rest of the info given in this statement cannot be used for calculating the speed of the train, because the two trains might run at different speed.

III gives, speed =	200	m/sec = 20 m/sec =		20 x	18	km/hr = 72 km/hr.
	10				5

II gives, time taken =		558	hrs =	31	hrs = 7	3	hrs = 7 hrs 45 min.
		72		4		4

So, the train will reach city X at 3 p.m.

Hence II and III only gives the answer.

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What is the speed of the train?
I.	The train crosses a tree in 13 seconds.
II.	The train crosses a platform of length 250 metres in 27 seconds.
III.	The train crosses another train running in the same direction in 32 seconds.

A:

I and II only

B:

II and III only

C:

I and III only

D:

Any two of the three

Answer: A

Let the speed of the train be x metres/sec.

Time taken to cross a tree =	Length of the train
	Speed of the train

Time taken to cross a platform =	(Length of the train + Length of the Platform)
	Speed of the train

I gives, 13 =	l	13x.
	x

II gives 27 =	l + 250
	x

	13x + 250	= 27
	x

x =	125	m/sec.
	7

Thus I and II give the speed of the train.

The correct answer is (A.)

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What is the speed of the train?
I.	The train crosses a signal pole in 18 seconds.
II.	The train crosses a platform of equal length in 36 seconds.
III.	Length of the train is 330 metres.

A:

I and II only

B:

II and III only

C:

I and III only

D:

III and either I or II only

Answer: D

Let the speed of the train be x metres/sec.

Time taken to cross a signal pole =	Length of the train
	Speed of the train

Time taken to cross a platform =	(Length of the train + Length of the Platform)
	Speed of the train

Length of train = 330 m.

I and III give, 18 =	330	x =	330	m/sec =	55	m/sec.
	x		18		3

II and III give, 36 =	2 x 330	x =	660	m/sec =	55	m/sec.
	x		36		3

Correct answer is (D).

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What is the length of a running train?
I.	The train crosses a man in 9 seconds.
II.	The train crosses a 240 metre long platform in 24 seconds.

A:

I alone sufficient while II alone not sufficient to answer

B:

II alone sufficient while I alone not sufficient to answer

C:

Either I or II alone sufficient to answer

D:

Both I and II are not sufficient to answer

Answer: E

Time taken by train to cross a man =	Length of train	Speed =	l	....(i)
	Speed of train		9

Time taken by train to cross a platform =	(Length of train + Length of platform)	Speed =	l + 240	....(ii)
	Speed of train		24

From (i) and (ii), we get	l	=	l + 240	.
	9		24

Thus, l can be obtained. So both I and II are necessary to get the answer.

The correct answer is (E).

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Questions for: Problems On Trains