The document contains various problems related to time and distances for trains, including calculating the time taken for trains to cross poles and bridges, determining the lengths of trains, and finding when trains traveling towards each other will meet. It provides formulas and examples for relative speed calculations in both opposite and same direction scenarios. Solutions to the problems are included, showing step-by-step calculations and final answers.

1. Time and Distances - 3

2. 1. Races and Games
2. Problems on Trains
3. Boats and Streams
Time and Distances

3. Problems on Trains

4. 1. A train crosses a pole in 12 sec. It crosses a bridge of length 300m in 27
sec. what is the time taken by the train to cross a bridge of length of 600m?
2. A train crosses a bridge of length 122m in 17 sec. it crossed another bridge
of length 210m in 25 sec. find the length of the train?
3. A train travelling at a speed of 54kmph crosses a platform in 36 sec and a
man standing on the platform in 20 sec. find the length of the platform?
4. A train of length 240m travelling at a speed of 64kmph overtakes a man
running at a speed of 10 kmph in __ sec ?
5. A train starts from a station X at 6am and reaches another station Y at 10
am. Another train starts from station Y at 8am and reaches station ‘X’ at
11:30am. At what time do the trains cross each other?

5. A train crosses a pole in 12 sec. It crosses a bridge of length 300m in 27 sec.
what is the time taken by the train to cross a bridge of length of 600m?
Ans :
NOTE:
• To cross a pole, A train has to travel a distance equal to length of train.
• To cross a bridge, A train has to travel a distance equal to length of train +
length of the bridge.
12 12 15 12 ?(30)
Time taken by the train to cross a bridge of length of 600m = 42sec
1.
Time taken by the train to cross a bridge of length of 600m = 42sec
300 – 15
600 – 30

6. A train crosses a bridge of length 122m in 17 sec. it crossed another
bridge of length 210m in 25 sec. find the length of the train?
2.
Ans :
NOTE:
• To cross a pole, A train has to travel a distance equal to length of train.
• To cross a bridge, A train has to travel a distance equal to length of train +
length of the bridge.
? x 17-x x 25-x
 8 sec – 88m
 17 sec - ? (187m)
 Length of the train = 187 – 122 = 65m
300 – 15
600 – 30
Length of the train = 65m

7. A train travelling at a speed of 54kmph crosses a platform in 36 sec and a
man standing on the platform in 20 sec. find the length of the platform?
3.
Ans :
20 20 16
 Length of the platform = 15*16 = 240m
Length of the platform = 240m
54kmph– 15m/sec

8. Relative speed: Speed of the body W.R.T to another body
• If 2 bodies A and B are travelling at speeds of ‘x’ kmph and ‘y’ kmph
respectively
• In opposite direction:
Speed of A W.R.T to B = x + y kmph
• In same direction :
Speed of A W.R.T to B = x - y kmph
• If 2 trains of lengths and are travelling at a speed of and respectively
• In opposite direction:
Time taken by two trains to cross each other = kmph
• In same direction :
Time taken by two trains to cross each other = kmph (if )

9. A train of length 240m travelling at a speed of 64kmph overtakes a man
running at a speed of 10 kmph in __ sec ?
4.
Time taken by the train = 16 sec
Ans :
Train and man are running in the same direction
 Relative speed = 64 – 10 = 54kmph = 15m/sec
 Time taken by the train = = 16 sec
54kmph– 15m/sec

10. A train starts from a station X at 6am and reaches another station Y at
10 am. Another train starts from station Y at 8am and reaches station
‘X’ at 11:30am. At what time do the trains cross each other?
5.
Ans :
= 4 hrs, = 3 ½ hrs : = 4 : = 8 : 7
: = 7 : 8
Assume d = 8 7 = 56km( d = s t)
=> = 56/4 = 14kmph = 56/3.5 = 16kmph
Relative speed = 14 +16 = 30kmph
By 8:00 am the 1st train reaches half of the distance and
2nd train has yet to start
28 28
6 10
11:30 8
8

11. Relative speed = 30kmph
=> 30 km – 1hr
28 km - ? (56min)
=> In the second half journey after 56 min the trains will
cross each other i.e. 8:56am.
30 – 60min
28 – 56min
Trains will cross each other at 8:56am.

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Problems for practice are given in the description of the video.

13. Practice problems
on Trains

14. Two trains of equal length cross a pole in 4 sec and 5sec respectively. What
is the time taken by the two trains to cross each other travelling in opposite
direction?
Two trains of lengths 225m and 275m respectively travelling in opposite
direction cross each other in 10 sec. If they travel in the same direction, then
the faster train over takes the slower train in 50 sec. find the speed of the
faster train?
A train starts from a station X at 8am and reaches another station Y at 10:30
am. Another train starts from station Y at 8:15am and reaches station ‘X’ at
10:15am. At what time do the trains cross each other?
A train of length 240m travelling at a speed of 64kmph overtakes a man
running at a speed of 10 kmph in __ sec ?
1.
2.
4.
3.

15. Two trains of equal length cross a pole in 4 sec and 5sec respectively.
What is the time taken by the two trains to cross each other travelling in
opposite direction?
1.
The time taken by the two trains to cross each other = 40/9 sec
Let the length of the train =
= , = =
Time taken in opposite = = = sec
Ans :

16. Two trains of lengths 225m and 275m respectively travelling in opposite
direction cross each other in 10 sec. If they travel in the same direction,
then the faster train over takes the slower train in 50 sec. find the speed
of the faster train?
2.
speed of the faster train = 30 m/sec
= 225m = 275m
 Speed in opposite = = 50m/sec = +
 Speed in same direction = = 10m/sec = -
 = 30 m/sec = 20 m/sec
Ans :

17. A train starts from a station X at 8am and reaches another station Y at
10:30 am. Another train starts from station Y at 8:15am and reaches
station ‘X’ at 10:15am. At what time do the trains cross each other?
3.
Ans :
= 2 ½ hrs, = 2 hrs : = : 2 = 5 : 4
: = 4 : 5
Assume d = 4 5 = 20km( d = s t)
=> = 20/2.5 = 8kmph = 20/2= 10kmph
Relative speed = 8 +10 = 18kmph
By 8:15 am the 1st train reaches 2km of the distance and
2nd train has yet to start
2 18
8 10:30
10:15 8:15

18. A train of length 220m travelling at a speed of 60kmph will cross a man
running at a speed of 12 kmph in opposite direction in __ sec ?
4.
Time taken by the train to over take the man = 11 sec
Ans :
Train and man are running in the opposite direction
 Relative speed = 60 + 12 = 72kmph = 20m/sec
 Time taken by the train = = 11 sec
72kmph– 20m/sec

19. Relative speed = 18kmph
=> 18 km – 1hr
=> In the second half journey after 1 hr the trains will
cross each other i.e. 9:15am.
Trains will cross each other at 9:15am.

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