# Problems on Trains

Problems on Trains are very important topic of aptitude section for all examinations. To understand the concepts of Problems on Trains and the questions related to Problems on Trains, you need to work hard. That is why candidates need to practice the questions based on Trains carefully.

The Problems on Trains Tricks and Examples provided here will help you to succeed in SSC, Banking, Railway Examination, Defense Examination or other examinations, because these types of questions are often asked in examinations. Problems on Trains related to all types of examinations are available here. You can prepare for the examinations through this website to earn marks in reckless examinations.

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## Problems on Trains

Problems on Trains Concept

• Length of the Train: The lengths of the two trains are always added.

Length Of Train A + Length Of Train B

• Distance covered by the Train when crossing a Bridge or Platform: The distance travelled by the train to clear a platform or a bridge is equal to the sum of the lengths of the train and the platform or the bridge.
• Opposite Direction: Running in opposite direction, time taken by two trains of length km and  km and speeds  km/hr and  km/hr respectively to cross each other is given by, • Crossing Time and Speed: If two trains X and Y starting from A and B and run towards each other and take a and b hours to reach B and A respectively after crossing each other then,  Problems on Trains Formulas

1. km/hr to m/s conversion: 2. m/s to km/hr conversion: 3. Time taken by a train of length l metres to pass a pole or 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 l metres to pass a stationery object of length b metres is the time taken by the train to cover (l + b) metres.

5. Suppose two trains or two objects bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed is = (u – v) m/s.

6. Suppose two trains or two objects bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (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:

The time taken by the trains to cross each other = 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 = 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: Some Examples On Problems On Trains

Question 1: A train passes two bridges of length 1000 m and 600 m in 120 seconds and 80 seconds respectively. The length of the train.

Solution: Distance covered in 120 second = 1000 + length of train(l)

Distance covered in 80 seconds = 600 + l

So, distance covered in 40 seconds = (1000 + l) – (600 + l)

= 400 m

Speed = 400/40 = 10 m/s

Distance covered in 80 second = 80 x 10 = 800 m

So, 600 + l = 800

Length of the train (l) = 200 m

Question 2: A train 500 m long is running at a speed of 72 km/hr. If it passes through a tunnel in 50 seconds, then the length of the tunnel is :

Solution: First convert speed in m/s

So, speed= 72 x (5/18)

= 20 m/s

Train covers the distance in 50 seconds = length of train + length of the tunnel(l)

500 + l = 20 x 50

500 + l = 1000

l = 500 m

Question 3: A train reaches from A to B in 5 hours travelling at a speed of 60 km/hr. If its speed is increased by 15 km/hr, then the time of journey is reduced by

Solution: Total distance = speed x time

=60 x 5 = 300 km

If speed increased then new speed= 60 + 15 = 75 km/hr

New time = Total distance/speed

= 300/75= 4 hour

Time reduced by 5 – 4 = 1 hour

Question 4: Delhi and Mumbai apart from each other 760 km.A train starts from Delhi at 9 am and travels towards Mumbai at speed 60 km/hr. Another train starts from Mumbai at 10 am and travels towards Delhi at speed 80 km/hr. At what time both will meet?

Solution: Total distance between D and M = 760 km.

A travels 1 hour before B so it travels = 60 x 1 = 60 km

Now the remaining distance D and M= 760 – 60 = 700 km

Relative speed = 60 + 80 = 140 km/hr

Time = 700 / 140

= 5 hour.

So, the time when they meet = 10 am + 5 hour = 3 pm

Question 5: Two trains 180 m and 120 m long respectively pass each other in 54 seconds when they run in the same direction and in 18 seconds when run in opposite directions. Find the speed of two trains.

Solution: Let the speed of 1st train is S1 and speed of 2nd train is S2

Time = total distance/ relative speed

1) In same direction

54 = (180 + 120) / (S1 – S2) * 5/18

(S1 – S2)54 = (300 * 18)/5

(S1 – S2) = 20

2) In opposite direction

9 = (180 + 120) / (S1 + S2) * 5/18

(S1 + S2)18 = (300 * 18)/5

(S1 + S2) = 60

from 1 and 2

S1 = 40 km/hr

S2 = 20 km/hr

Problems on Trains – Short Tricks

Shortcut 1 :

Speed  =  Distance / Time

Shortcut 2 :

Distance  =  Speed ⋅ Time

Shortcut 3 :

Time  =  Distance / Speed

Shortcut 4 :

If the speed is given km per hour and we want to convert it in to meter per second, we have to multiply the given speed by 5/18.

Example:

90 km/hr  =  90 ⋅ 5/18  =  25 meter/sec

Shortcut 5 :

If the speed is given meter per sec and we want to convert it in to km per hour, we have to multiply the given speed by 18/5.

Example:

25 meter/sec  =  25 ⋅ 18/5  =  90 km/hr

Shortcut 6 :

Let the length of the train be “L” meters.

Distance traveled to pass a standing man  =  L  meters

Shortcut 7 :

Let the length of the train be “L” meters.

Distance traveled to pass a pole  =  L  meters

Shortcut 8 :

Let the length of the train be “a” meters and the length of the platform be “b” meters.

Distance traveled to pass the platform is

=  (a + b) meters

Shortcut 9 :

If two trains are moving on the same directions with speed of “p” m/sec and “q” m/sec (here p > q), then their relative speed is

=  (p – q) m/sec.

Shortcut 10 :

If two trains are moving opposite to each other in different tracks with speed of “p” m/sec and “q” m/sec, then their relative speed is

=  (p + q) m/sec.

Shortcut 11 :

Let “a” and “b” are the lengths of the two trains.

They are traveling on the same direction with the speed “p” m/sec and “q” m/sec (here p > q),

then the time taken by the faster train to cross the slower train

=  (a + b) / (p – q)  seconds.

Shortcut 12 :

Let “a” and “b” are the lengths of the two trains.

They are traveling opposite to each other in different tracks with the speed “p” m/sec and “q” m/sec,

then the time taken by the trains to cross each other

=  (a + b) / (p + q)  seconds.

Shortcut 13 :

Two trains leave at the same time from the stations P and Q and moving towards each other.

After crossing, they take “p” hours and “q” hours to reach Q and P respectively.

Then the ratio of the speeds of two trains

=  Square root (q) : Square root (p)

Shortcut 14 :

Two trains are running in the same direction/opposite direction.

The person in the faster train observes that he crosses the slower train in “m” seconds.

Then the distance covered in “m” seconds in the relative speed is

=  Length of the slower train

Shortcut 15 :

Two trains are running in the same direction/opposite direction.

The person in the slower train observes that the faster train crossed him “m” seconds.

Then the distance covered in “m” seconds in the relative speed is

=  Length of the faster train

Rules on Problem On Trains

Rule 1: When two trains are moving in opposite directions, then relative speed will be the addition of their individual speeds.

Rule 2: When two trains are moving in same direction, then relative speed will be the subtraction of their individual speeds.

Rule 3: On passing a platform by a certain train the net distance traveled is the sum of length of train and the length of platform both.

Rule 4: When a train passes through a pole or person standing, net distance traveled to pass is the length of the train

Types of Questions on Train Problems

Over the years, the exam pattern has changed with the increase in the number of applicants and every year candidate’s notice a new pattern or format in which questions are asked for various topics in the syllabus.

It is important that a candidate is aware of the types in which a question may be framed or asked in the examination to avoid any risk of losing marks.

Thus, given below are the type of questions which may be asked from the train-based problems:

1. Time Taken by Train to Cross any stationary Body or Platform – Calculate the time taken by a train to cross a stationary body like a pole or a standing man or a platform/ bridge.
2. Time Taken by 2 trains to cross each other –Time two trains might take to cross each other.
3. Train Problems based on Equations – Two cases may be given in the question and the candidates will have to form equations based on the condition given.

Problems on Trains Practice Question

Ques1: A man’s speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man’s speed against the current is :

A) 9.5 km/hr

B) 10 km/hr

C) 10.5 km/hr

D) 11 km/hr

 Explanation:Man’s rate in still water = (15 – 2.5) km/hr = 12.5 km/hr.Therefore,  Man’s rate against the current = (12.5 – 2.5) = 10 km/hr.

Ques2: A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?

A) 60

B) 62

C) 64

D) 65

 Explanation:Relative speed =280/9  m / sec = (280/9*18/5)  kmph = 112 kmph.Speed of goods train = (112 – 50) kmph = 62 kmph.

Ques3: Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is

A) 42

B) 36

C) 28

D) 20

 Explanation:Distance covered = 120+120 = 240 mTime = 12 sLet the speed of each train = v. Then relative speed = v + v = 2v2v = distance/time = 240/12 = 20 m/sSpeed of each train = v = 20/2 = 10 m/s= 10 × 36/10 km/hr = 36 km/hr

Ques4: A train of length 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?

A) 10

B) 8

C) 6

D) 4

 Explanation:Distance = 110 mRelative speed = 60 + 6 = 66 kmph (Since both the train and the man are in moving in opposite direction)= (66*5/18)  m/sec = 55/3  m/secTime taken to pass the man = (100*3/55) = 6 s

Ques5: Two trains started at the same time, one from A to B and the other from B to A . If they arrived at B and A respectively 4 hours and 9 hours after they passed each other the ratio of the speeds of the two trains was

A) 2:1

B) 3:2

C) 4:3

D) 5:4

 Explanation:Note : 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)Therefore, Ratio of the speeds of two trains = √9:√4= 3 : 2

Ques6: A train travelling at a speed of 75 mph enters a tunnel 312miles long. The train is 14mile 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 =154milesTime taken = (154*75)hrs = 120 hrs =(120*60)min = 3 min

Ques7: 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

 Explanation:Assume both trains meet after x hours after 7 amDistance covered by train starting from P in x hours = 20x kmDistance covered by train starting from Q in (x-1) hours = 25(x-1)Total distance = 110=> 20x + 25(x-1) = 110=> 45x = 135=> x= 3Means, they meet after 3 hours after 7 am, ie, they meet at 10 am

Ques8: 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

 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.

Ques9: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is ?

A) 45 kmph

B) 25 kmph

C) 30 kmph

D) 50 kmph

 Explanation:Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec.[(25/2) x (18/5)] km/hr = 45 km/hr.Let the speed of the train be ‘S’ km/hr.Then, relative speed = (S – 5) km/hr.S – 5 = 45 => S = 50 km/hr.

Ques10: 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

 Explanation:Speed =[ 72 x (5/18) ]m/sec= 20 m/sec.Time = 26 sec.Let the length of the train be x metres.Then,[ (x+250)/26 ]= 20=> x + 250 = 520=> x = 270.

Ques11: 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.

Ques12: 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.

Ques13: 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

 Explanation:Let the length of the train be x metres and its speed by y m/sec.Then, x/y = 8 => x = 8yNow, (x+264)/20 = y8y + 264 = 20yy = 22.Speed = 22 m/sec = (22*18/5) km/hr = 79.2 km/hr.

Ques14: 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 = (120/10)m/sec = 12 m/secSpeed of train 2 =(120/15)m/sec  = 8 m/secif they travel in opposite direction, relative speed = 12 + 8 = 20 m/secdistance covered = 120 + 120 = 240 mtime = distance/speed = 240/20 = 12 sec

Ques15: 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/secTime taken to pass the man = [110*(3/55)]m/sec = 6 sec.

Ques16: 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

 Explanation:Given speed = 63 km/hr = 63×518=352 m/sLet the length of the bridge = x mtsGiven time taken to cover the distance of (170 + x)mts is 30 sec.We know speed = distancetimem/s⇒352=170+x30–>  x = 355 mts.

Ques17: 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

 Explanation:Relative speed = (120 + 80) km/hr=(200*5/18)m/s = (500/9)m/sLet the length of the other train be x metres.Then, x+270/9 = 500/9=>  x + 270 = 500=>  x = 230.

Ques18: A train running at the speed of 40 km/hr crosses a signal pole in 9 seconds. Find the length of the train ?

1. A) 90 mts
2. B) 150 mts
3. C) 120 mts
4. D) 100 mts

 Explanation:We know that   Speed=distance/timedistance= speed * time⇒ d=(40×518)×9d= 100 mts.

Ques19: 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  ?

1. A) 10 sec
2. B) 11 sec
3. C) 12 sec
4. D) 8 sec

 Explanation:Relative Speed = 60 -40 = 20 x 5/18 = 100/18Time = 50Distance = 50 x 100/18 = 2500/9Relative Speed = 60 + 40 = 100 x 5/18Time = 2500/9 x 18/500 = 10 sec.

Ques20: 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 ?

1. A) 80 kms
2. B) 60 kms
3. C) 45 kms
4. D) 32 kms