Problems on trains is a special case on time & distance aptitude problems. Students could find some useful techniques to solve such problems here

1. C.S.VEERARAGAVAN
SIXPHRASE – The Finishing School
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Problems on
TRAINS

2. How much time did the man spend walking?
Each day a man meets his wife at the train station
after work, and then she drives him home.
She always arrives exactly on time to pick him up.
One day he catches an earlier train and arrives at
the station an hour early.
He immediately begins walking home along the
same route the wife drives.
Eventually his wife sees him on her way to the
station and drives him the rest of the way home.
When they arrive home the man notices that they
arrived 20 minutes earlier than usual.
Answer at the end of Session
Discussion online.

3. Basic concepts
To convert from km/hr to m/sec Multiply by
𝟓
𝟏𝟖
To convert from m/sec to Km/hr
Multiply by
𝟏𝟖
𝟓

4. Train crossing a man or signal post
• 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.
• Time taken =
𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒕𝒉𝒆 𝑻𝒓𝒂𝒊𝒏
𝑺𝒑𝒆𝒆𝒅 𝒐𝒇 𝒕𝒉𝒆 𝑻𝒓𝒂𝒊𝒏
• Find the time taken by the train of 100 m long running
at the speed of 30 km/hr to pass a man standing near
the railway line.
• Speed of the Train = 30 X
5
18
=
25
3
sec.
• Time taken =
100
25
3
=
300
25
=12 sec.

5. • 1.A train running at the speed of 60 km/hr
crosses a pole in 9 seconds. What is the length
of the train?
• A. 120 metres B. 180 metres
• C. 324 metres D. 150 metres
• Speed of the Train = 60 x
5
18
=
50
3
m/sec
• Length of the Train = 9 x
50
3
=150 metres.
Train crossing a man or signal post

6. • 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.
• Time Taken=
𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒕𝒉𝒆 𝑻𝒓𝒂𝒊𝒏+𝑳𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒐𝒃𝒋𝒆𝒄𝒕
𝑺𝒑𝒆𝒆𝒅 𝒐𝒇 𝒕𝒉𝒆 𝑻𝒓𝒂𝒊𝒏
• 6) A train 360 m long is running at a speed of 45
km/hr. in what time will it pass a bridge 140 m
long?
• Speed of the Train = 45 x
5
18
=
25
2
m/sec.
• Time taken =
360+140
25
2
=
500
25
2
=
1000
25
=40 sec.
Train crossing a stationery object (platform/bridge)

7. • 5.A train 240 m long passes a pole in 24
seconds. How long will it take to pass a
platform 650 m long?
• A. 65 sec B. 89 sec
• C. 100 sec D. 150 sec
• Speed of the Train =
240
24
=10 m/sec.
• Time taken to pass platform =
240+650
10
=89 sec.
Train crossing a stationery object (platform/bridge)

8. • 2.The length of the bridge, which a train 130
metres long and travelling at 45 km/hr can cross
in 30 seconds, is:
• A. 200 m B. 225 m
• C. 245 m D. 250 m
• Speed of the Train =45 x
5
18
=
25
2
m/sec.
• Let the length of the bridge be x metres.
• Then
130+𝑥
30
=
25
2
• 2(130 + x) =750
• X = 245 metres.
Train crossing a stationery object (platform/bridge)

9. • 16.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:
• A.130 B. 360 C. 500 D. 540
• Speed = 78 x
5
18
=
65
3
m/sec.
• Let the length of tunnel be x metres.
• Then
800+𝑥
60
=
65
3
.
• 3(800 + x) = 3900
• => x = 500 metres.
Train crossing a stationery object (platform/bridge)

10. • 15.A train travelling at a speed of 75 mph enters
a tunnel 3
1
2
miles long. The train is
1
4
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
• Total distance covered =
7
2
+
1
4
=
15
4
miles.
• Time taken to pass=
15
4𝑋75
=
1
20
hrs = 3min.
Train crossing a stationery object (platform/bridge)

11. • 11.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
• Speed of the Train =72 x
5
18
=20 m/sec.
• Let the length of the Train be x m.
• Then
𝑥+250
20
=26
• X +250 = 520
• X=270 metres.
Train crossing a stationery object (platform/bridge)

12. • 4.A train passes a station platform in 36 seconds and a
man standing on the platform in 20 seconds. If the
speed of the train is 54 km/hr, what is the length of the
platform?
• A. 120 mB. 240 m
• C. 300 mD. None of these
• Speed of the Train = 54 x
5
18
=15 m/sec.
• Length of Train=Time takenxspeed=20x15=300 m
• Let the length of the platform be x.
• Then
300+𝑥
15
= 36.
• X = 540 – 300 = 240 m
Train crossing a stationery object (platform/bridge)

13. • Time of rest per hr=
𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒊𝒏 𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒔𝒑𝒆𝒆𝒅
𝑺𝒑𝒆𝒆𝒅 𝒘𝒊𝒕𝒉𝒐𝒖𝒕 𝒔𝒕𝒐𝒑𝒑𝒂𝒈𝒆
x60
15. Excluding stoppages, the speed of a bus is 54
kmph and including stoppage, it is 45 kmph. For
how many minutes does the bus stop per hour?
Time of rest per hour =
54−45
54
𝑥60= 10 minutes

14. Problems on Two Trains
Move in Parallel/Same & opposite directions

15. Problems on Two trains
• 3. Two trains running in opposite directions cross a man standing on
the platform in 27 seconds and 17 seconds respectively and they
cross each other in 23 seconds. The ratio of their speeds is:
• A. 1 : 3 B. 3 : 2
• C. 3 : 4 D. None of these
• Let the speeds of the two trains be x m/sec and y m/sec
respectively.
• Then, length of the first train = 27x metres,
• length of the second train = 17y metres.
•
27𝑥+17𝑦
𝑥+𝑦
=23.
• 27x +17y=23x + 23y
• 4x = 6y
• x:y = 3:2.
Time taken to cross each other =
𝑆𝑢𝑚 𝑜𝑓 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑇𝑟𝑎𝑖𝑛𝑠
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑆𝑝𝑒𝑒𝑑
If both trains run in opposite direction, then
relative speed is sum of their speeds.
If they move in the same direction, then
relative speed is difference of their speeds.

16. • 7. 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
• Time taken to cross each other=
2𝑋 𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑇𝑟𝑎𝑖𝑛
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑆𝑝𝑒𝑒𝑑
• Relative Speed = 46 – 36 = 10 km/hr =10x
5
18
=
25
9
• Length of the Train =
36𝑋
25
9
2
=
36𝑋25
18
=50m.
Problems on Two trains

17. • 10. 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
• Relative speed=120+80=200kmph=200x
5
18
=
500
9
• Let length of other train be x m.
• Time taken = 9 =
270+𝑥
500
9
500=270+x x = 230m.
Problems on Two trains

18. • 8. Two trains are moving in opposite directions @ 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. 36 B. 45
• C. 48 D. 49
• Time taken to cross each other=
𝑆𝑢𝑚 𝑜𝑓𝐿𝑒𝑛𝑔𝑡ℎ𝑠 𝑜𝑓 𝑇𝑟𝑎𝑖𝑛𝑠
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑆𝑝𝑒𝑒𝑑
• Sum of lengths = 1100+900= 2000m.
• Relative Speed = 60+90=150km/hr=150x
5
18
=
125
3
• Time taken =
2000
125
3
=
2000𝑋3
125
=48 seconds.
Problems on Two trains

19. • 12.Two trains, each 100 m long, moving in opposite
directions, cross each other in 8 seconds. If one is
moving twice as fast the other, then the speed of the
faster train is:
• A. 30 km/hr B. 45 km/hr
• C. 60 km/hr D. 75 km/hr
• Let the speed of the slower train be x m/sec.
• Then, speed of the faster train = 2x m/sec.
• Relative speed = (x + 2x) m/sec = 3x m/sec.
•
100+100
8
=3x
• X=
25
3
and speed of faster train is
50
3
𝑥
18
5
=60km/hr.
Problems on Two trains

20. • 13.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
• Relative Speed of the Train =
60+40=100kmph=100x
5
18
=
250
9
m
• Time taken to cross each other =
140+160
250
9
=
300𝑋9
250
•
54
5
=10.8 seconds.
Problems on Two trains

21. • 9. A jogger running at 9 kmph alongside a railway track
in 240 metres ahead of the engine of a 120 metres long
train running at 45 kmph in the same direction. In how
much time will the train pass the jogger?
• A. 3.6 sec B. 18 sec
• C. 36 sec D. 72 sec
• Time taken to cross each other=
𝑇𝑜𝑡𝑎𝑙 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑐𝑜𝑣𝑒𝑟𝑒𝑑
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑆𝑝𝑒𝑒𝑑
• Total distance covered = 120+240= 360 metres.
• Relative Speed = 45 – 9 = 36kmph=36x
5
18
=10 m/sec
• Time taken to cross =
360
10
= 36 seconds.
Problems on Two trains objects moving.

22. • 14.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 sec B. 6 sec
• C. 7 sec D. 10 sec
• Relative Speed =60+6=66kmph=66x
5
18
=
55
3
m/sec
• Time taken to cross =
110
55
3
=6 sec.
Problems on Two trains objects moving.

23. Train crossing a lengthy object & a post /person.
• 17. A 300 metre long train crosses a platform in
39 seconds while it crosses a signal pole in 18
seconds. What is the length of the platform?
A.320m B.350m C.650 m D. Data inadequate
Time taken to cross platform
=
𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑃𝑙𝑎𝑡𝑓𝑜𝑟𝑚
𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑇𝑟𝑎𝑖𝑛
𝑥
𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑇𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 𝑇𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
• 39 =
𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑃𝑙𝑎𝑡𝑓𝑜𝑟𝑚
300
𝑋
39𝑋18
39−18
• Length of platform =
39𝑋300𝑋21
39𝑋18
=350m

24. • 18. 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
Time taken to cross platform = 𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑃𝑙𝑎𝑡𝑓𝑜𝑟𝑚
𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑇𝑟𝑎𝑖𝑛
𝑥
𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑇𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 𝑇𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
• 25 =
100
𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑇𝑟𝑎𝑖𝑛
𝑥
15𝑋25
25−15
• Length of Train =
100𝑋15𝑋25
10𝑋25
= 150m.
Train crossing a lengthy object & a post /person.

25. • 19. 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
Time taken to cross platform
=
𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑃𝑙𝑎𝑡𝑓𝑜𝑟𝑚
𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑇𝑟𝑎𝑖𝑛
𝑥
𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑇𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 𝑇𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
• 20 =
264
8𝑋𝑠𝑝𝑒𝑒𝑑
𝑋
20𝑋8
20−8
• Speed of the train =
264𝑋20𝑋8
8𝑋12𝑋20
= 22 m/sec.
• Hence speed =22 X
18
5
=79.2 km/hr.
Train crossing a lengthy object & a post /person.

26. • 20. How many seconds will a 500 metre long
train take to cross a man walking with a speed
of 3 km/hr in the direction of the moving train
if the speed of the train is 63 km/hr?
• A. 25 B. 30
• C. 40 D. 45
• Relative speed = 63–3=60kmph=60x
5
18
=
50
3
• Time taken to cross =
500
50
3
=30 seconds.
Problems on Two trains objects moving.