Two trains of equal length are moving in same direction on parallel tracks at speed of 92 km

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Exercise :: Problems on Trains - General Questions
Exercise :: Problems on Trains - General Questions
Exercise :: Problems on Trains - General Questions
Exercise :: Problems on Trains - General Questions
Exercise :: Problems on Trains - General Questions
Exercise :: Problems on Trains - General Questions

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Discussion

Two trains of equal length are moving in same direction on parallel tracks at speed of 92 km/hr and 72 km/hr respectively. The faster train crosses the slower train in 18 seconds. Find the length of each train.

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Workspace

Answer : Option D)

Answer with explanation:

Let the length of each train is X.

Distance covered = 2X (sum of the length of trains)

Relative Speed of faster train= 92 − 72 = 20 km/hr

Relative Speed in m/s = 20 x

GIVEN:

Two trains of equal lengths moving in the same direction pass each other in 2 minutes 56 seconds. Moving in opposite direction, they pass each other in 45 seconds.

CONCEPT:

Basic concept of Trains.

FORMULA USED:

Relative speed = (a + b) for opposite directions

Relative speed = (a - b) for same directions

Where a and b are speed of train

Speed = Distance / Time

CALCULATION:

Let the speed of the faster train be v1 m/s and that of the slower train be v2 m/s.

Let the length of trains be D meters each

2 minutes and 56 seconds = 176 seconds

According to the question:

2D = (v1 - v2) × 176

And,

2D = (v1 + v2) × 45

Equating both we get,

176v1 - 176v2 = 45v1 + 45v2

⇒ 131v1 = 221v2

⇒ v1/v2 = 221 / 131

∴ Ratio of the speeds of faster train to the slower train is 221 : 131

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Exercise :: Problems on Trains - General Questions

Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:

A.	50 m
B.	72 m
C.	80 m
D.	82 m

Answer: Option A

Explanation:

Let the length of each train be x metres.

Then, distance covered = 2x metres.

Relative speed = (46 - 36) km/hr

=		10 x	5	m/sec
18

=		25	m/sec
9

	2x	=	25
36	9

2x = 100

x = 50.

Page 2

Exercise :: Problems on Trains - General Questions

11.

A 270 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

A.	230 m
B.	240 m
C.	260 m
D.	320 m
E.	None of these

Answer: Option A

Explanation:

Relative speed = (120 + 80) km/hr

=		200 x	5	m/sec
18

=		500	m/sec.
9

Let the length of the other train be x metres.

x + 270 = 500

x = 230.

12.

A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train?

A.	230 m
B.	240 m
C.	260 m
D.	270 m

Answer: Option D

Explanation:

Speed =		72 x	5	m/sec	= 20 m/sec.
18

Time = 26 sec.

Let the length of the train be x metres.

x + 250 = 520

x = 270.

Page 3

Exercise :: Problems on Trains - General Questions

17.

A train 800 metres long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 minute, then the length of the tunnel (in meters) is:

Answer: Option C

Explanation:

Speed =		78 x	5		m/sec	=		65		m/sec.
18	3

Time = 1 minute = 60 seconds.

Let the length of the tunnel be x metres.

Then,		800 + x		=	65
60	3

3(800 + x) = 3900

x = 500.

Page 4

Exercise :: Problems on Trains - General Questions

22.

Two goods train each 500 m long, are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one.

A.	12 sec
B.	24 sec
C.	48 sec
D.	60 sec

Answer: Option B

Explanation:

Relative speed =

= (45 + 30) km/hr

=		75 x	5		m/sec
18

=		125		m/sec.
6

We have to find the time taken by the slower train to pass the DRIVER of the faster train and not the complete train.

So, distance covered = Length of the slower train.

Therefore, Distance covered = 500 m.

Required time =		500 x	6		= 24 sec.
125

Page 5

Exercise :: Problems on Trains - General Questions

27.

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:

A.	45 m
B.	50 m
C.	54 m
D.	72 m

Answer: Option B

Explanation:

2 kmph =		2 x	5		m/sec =	5	m/sec.
18	9

4 kmph =		4 x	5		m/sec =	10	m/sec.
18	9

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

Then,		x		= 9 and		x		= 10.

9y - 5 = x and 10(9y - 10) = 9x

9y - x = 5 and 90y - 9x = 100.

On solving, we get: x = 50.

Length of the train is 50 m.

28.

A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?