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TRAINS
a km /hr =
18
5
a m/s.
a m/s =
5
18
a km / hr.
• 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...
• 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...
Time Taken
• Time taken by a train of length l metres to pass a stationery object of
length b metres is the time taken by ...
Time Taken
A train of length 300m travels at a speed of 36 kmph. In how
many seconds does it cross a bridge of length 700m...
• When two trains are moving in opposite
directions, their speeds should be added to find
the relative speed. When two tra...
• If two trains of length a metres and b metres
are moving in opposite directions at u m/s and
v m/s, then time taken by t...
• Some times, we can calculate without using
any definite formula but straightly work out.
• P and Q are 300 km apart. At ...
• Example 3. (Refer Problem 13)
• Two trains 140m and 160m long run at the
speed of 60 km/hr and 40 km/hr respectively
in ...
• If two trains of length a metres and b metres
are moving in same directions at u m/s and v
m/s, then time taken by the f...
• Example 4.
• Two trains of the same but with different speeds pass a
telegraph post in 8 seconds and 10 seconds respecti...
• If two trains (or bodies) start at the same time
from points A and B towards each other and
after crossing they take a a...
• Example 5.
• Two trains, one from Howrah to Patna and the other from
Patna to Howrah, start simultaneously. After they m...
Example 6.
Two trains start at the same time from Cuttack and Delhi and move toward each other at
the rate of 70 km/h and ...
• Time of rest per hour = Difference in average speed
Speed without stoppage
Example 7.
Without stoppage a train travels a...
• Length of the train =
Speed of the train = Product of speed- Product of times
Difference in times
Example 8.
A train pas...
• Length of the train = Timetopassapole×Length of platform
Difference in time to cross a pole and platform
Example 9.
A tr...
Speed of the 1st train=Speed of the 2nd train x
Timetaken by firsttrain after meeting
Timetaken by secondtrain after meeti...
Example 12.
Two places A and B are 180 km apart. A train leaves P for Q and at the same time
another train leaves B to A. ...
• A car moves at the speed of 80 km/hr. what is
the speed of car in metres per second? a)
8m/s b) m/s c) m/s d) None f the...
• Sound is said to travel in air at about 1100 feet
per second. A man hears the axe striking the
tree, seconds after he se...
• A salesman travels a distance of 50 km in 2
hours 30 minutes. How much faster, in
kilometres per hour, on an average, mu...
• A person travels from P to Q at a speed of 40
kmph and returns by increasing his speed by
50%. What is his average speed...
• A train can travel 50% faster than a car. Both start
from point A at the same time and reach point B 75
kms away from A ...
Rearrange two to make four identical
squares
Trains full
Trains full
Trains full
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Trains full

problem on trains, aptitude

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Trains full

  1. 1. TRAINS
  2. 2. a km /hr = 18 5 a m/s. a m/s = 5 18 a km / hr.
  3. 3. • 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 = Example 1. 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. Lengthof thetrain Speedof thetrain
  4. 4. • 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 = Example 1. 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 train= 18 5 30 m/sec= 3 25 m/sec. Required time taken = 100 25 3 = 3100 25 sec = 12 sec. Lengthof thetrain Speedof thetrain
  5. 5. Time Taken • 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. • Example 2. • A train is moving at a speed of 132 km/hr. If the length of the train is 110 metres, how long will it take to cross a railway platform 165 metres long? Speed of the train = 5132 18 m/sec = 110 3 m/sec. Distance covered in passing the platform = (110 + 165)m = 275 m. Time taken = 3275 110 sec = 15 2 sec = 7 1 2 sec.
  6. 6. Time Taken A train of length 300m travels at a speed of 36 kmph. In how many seconds does it cross a bridge of length 700m? Distance travelled = Length of the Train + Length of the Bridge = 300 + 700 = 1000m
  7. 7. • When two trains are moving in opposite directions, their speeds should be added to find the relative speed. When two trains are moving in same directions, their speeds should be subtracted to find the relative speed. • Suppose two trains or two bodies moving in the same direction at u m/s and v m/s where u > v , then their relative speed = (u – v) m/s. • Suppose two trains or two bodies moving in the opposite directions at u m/s and v m/s where u > v , then their relative speed = (u + v) m/s.
  8. 8. • If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then time taken by the trains to cross each other = Required time= Sum of the lengths of two trains Relative speed of them a b u v 2× Product of their speeds Sum of their speeds
  9. 9. • Some times, we can calculate without using any definite formula but straightly work out. • P and Q are 300 km apart. At 8.00 am, buses X and Y left P and Q simultaneously for Q and P respectively. If the speeds of buses X and Y are 40 kmph and 60 kmph respectively, when do they meet? Time Travelled X Y Balance time travelled By X and Y In one hour 40 60 260,240 In Two hours 80 120 220,180 In Three hours 120 180 180,120
  10. 10. • Example 3. (Refer Problem 13) • Two trains 140m and 160m 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 = (60 + 40) km/hr = Distance covered in crossing each other = sum of the lengths= (140 + 160)m =300 m Required time 9 54300 sec sec 5250
  11. 11. • If two trains of length a metres and b metres are moving in same directions at u m/s and v m/s, then time taken by the faster train to cross the slower train = Sum of the lengths of two trains Relative speed of them 2× Product of their speeds Difference of their speeds
  12. 12. • Example 4. • Two trains of the same but with different speeds pass a telegraph post in 8 seconds and 10 seconds respectively. In what time will they cross each other when they are moving in: • (i) the same direction? (ii) opposite direction? 2 8 10 10 8 2 8 10 10 8 8 98 = 80 sec.Required time = Required time =
  13. 13. • 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) =
  14. 14. • Example 5. • Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is: • a) 2:3 b) 4:3 c) 6:7 d) 9:16. • Let us name the trains as A and B. Then, (A’s speed) : (B’s speed) =
  15. 15. Example 6. Two trains start at the same time from Cuttack and Delhi and move toward each other at the rate of 70 km/h and 80 km/h respectively. When they meet, it is found that one train has travelled 120 km more than the other. Find the distance between Delhi and Cuttack. Required distance = 80 70120 80 70
  16. 16. • Time of rest per hour = Difference in average speed Speed without stoppage Example 7. Without stoppage a train travels at an average speed of 90 km/h and with stoppage it covers the same distance at an average speed of 72 km/h. How many minutes per hour does the train stop? Time of rest per hour = = 12 minutes. Eg Pg 24 Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
  17. 17. • Length of the train = Speed of the train = Product of speed- Product of times Difference in times Example 8. A train passes two persons who are walking in the direction opposite which the train is moving at the rate of 6 m/s and 9 m/s in 7 seconds and 6 seconds respectively. Find the length of the train and speed of the train. Length of the train = =126 m. 9 6 7 6 7 6 Speed of the train = 9 6 7 6 7 6 =12 m/sec.
  18. 18. • Length of the train = Timetopassapole×Length of platform Difference in time to cross a pole and platform Example 9. A train passes a pole in 12 seconds and passes a platform 120m long in 20 seconds. Find its length. Required length = 12 120 180 . 20 12 m 18. A train speeds past a pole in 15 seconds and a platform 100m long in 25 seconds. Its length is
  19. 19. Speed of the 1st train=Speed of the 2nd train x Timetaken by firsttrain after meeting Timetaken by secondtrain after meetingExample 11. Two trains A and B start from Kolkata and Patna towards Patna and Kolkata respectively. After passing each other they take 8 hours and 2 hours to reach Patna and Kolkata respectively. If the train from Kolkata is moving at 50 km/h, then find the speed of the other train. Required speed = 850 2 = 100 km/h.
  20. 20. Example 12. Two places A and B are 180 km apart. A train leaves P for Q and at the same time another train leaves B to A. Both the trains meet 4 hours after they start moving. If the train travelling from A to B travels 5 km/h faster than the other train, find the speed of the two trains. Speeds of the trains = = 25 and 20. 180 4 5 180 4 5 2 4 2 4 and
  21. 21. • A car moves at the speed of 80 km/hr. what is the speed of car in metres per second? a) 8m/s b) m/s c) m/s d) None f these
  22. 22. • Sound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, seconds after he sees it strike the tree. How far is the man from the woodchopper? a)2197ft b) 2420 ft c) 2500 ft d) 2629 ft
  23. 23. • A salesman travels a distance of 50 km in 2 hours 30 minutes. How much faster, in kilometres per hour, on an average, must he travel to make such a trip in hour less time? a)10 b)20 c)30 d)None
  24. 24. • A person travels from P to Q at a speed of 40 kmph and returns by increasing his speed by 50%. What is his average speed for both trips? a)36kmph b)45kmph c)48kmph d)50 kmph
  25. 25. • A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is • a)100kmph b)110kmph c)120kmph d)130kmph.
  26. 26. Rearrange two to make four identical squares

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  • ashwanikumar524934

    Feb. 9, 2015
  • aanandkumarsahu

    May. 7, 2015
  • darshanprajapati315

    Sep. 18, 2015

problem on trains, aptitude

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