Sunday, August 16, 2015

Maths Problems on Trains- Part 4th

In the previous post of Problem based on trains we have discussed about some basic concepts of this chapter. Now we will see some more of the various frequently asked important question of this chapter in competition like SSC, Bank (IBPS), and Railways.
Important Types questions on Trains:-
Concept 3rd :- Relative speed Concept:-

Q10. Two trains can run at the speed of 54 km/hr and 36 km/hr respectively on parallel track. When they are running in opposite directions they pass each other in 10 secs. When they are running in the same direction, a person sitting in in the faster train observes that he passes the other train in 30secs. Find the length of the trains.

Sol.  the distance travelled by the trains to cross each other = sum of lengths of trains
distance = l1 + l2 where  l1 is the length of the train 1st
                                  and l2 is the length of the train 2nd
Analyse the given data in the question:
Speed of 1st train (x) = 54 kms./hr.
Speed of 2nd  train (y) = 36 kms./hr.     
Time taken by the trains to cross each other = 10 secs.

Relative speed (Trains moving in opposite direction) = 54 + 36 = 90 kms./hr.
                                                                                  = 90 × (5/18) = 25 m/sec.
Formula used in such questions:  Time taken = Total distance/(Relative speed)
Putting the values;
10 = (l1 + l2)/25
(l1 + l2) = 25 × 10 = 250
l1 + l2 = 250   .............................................. eq.no.1.
Time observed by the man in the faster train to cross the slower train = 30 secs.
Distance travelled by the man sitting in faster train = length of slower train
Relative speed (Trains moving in same direction) = 54 - 36 = 18 kms./hr.
                                                                                  = 18 × (5/18) = 5 m/sec.
Formula used in such questions:  Time taken = distance/(Relative speed)
Putting the values;
30 = distance(l2)/5
l2 = length of the slower train = 5 × 30 = 150 metres
length of the slower train = 150meters
From equation 1. We get,
l1 + 150 = 250
l1 = length of the faster train = 100 metres.
Hence the required lengths of both the trains are 100 m and 150 m respectively.

Concept 4th :- Train crossing a man with moving speed

Q11. A train 110 metres in length travels at 40km/hr. In what time will it cross a man who is walking at a speed of 4 km an hour.
(i)                 Same direction
(ii)               In the opposite direction?

Sol. Analyse the given data in the question:
Speed of the train = 40 km/hr.
Speed of the man = 4 km/hr.
Distance travelled by train in passing the moving man = length of the train = 110 m.
(i)                 Relative speed while both are moving in same direction = 40 – 4
                                                                              = 36 km/hr.
                                                                                   = 36 × (5/18) = 10 m/sec.
Time taken by the train to pass the moving man = Distance/ relative speed
                                                                                 = 110/10 = 11 secs.
(ii)               Relative speed while both are moving in opposite direction = 40 + 4
                                                                              = 44 km/hr.
                                                                                   = 44 × (5/18) = (110/9) m/sec.
Time taken by the train to pass the moving man = Distance/ relative speed
                                                                                 = 110/(110/9) = 9 secs.
Hence the required times are (i) 11 secs. And (ii) 9 secs.

Q12. A train running at 24 km/hr takes 30 seconds to pass a platform. Next, it takes 10 seconds to pass a man walking at 12 km/hr in the opposite direction. Find the length of the train.

Sol. Analyse the given data in the question:
Speed of the train = 24 km/hr.
Speed of the man = 12 km/hr.
Distance travelled by train in passing the moving man = length of the train.
Time taken by the train to cross the platform = 30 secs. (Not required to solve this question)
Time taken by the train to cross the man, moving in opposite direction = 10 secs.
Relative speed while both are moving in opposite direction = 24 + 12
                                                                              = 36 km/hr.
                                                                                   = 36 × (5/18) = 10 m/sec.
Time taken by the train to pass the moving man = Distance/ relative speed
                                                                            10 = distance/10.
Distance = length of the train = 10 × 10 = 100 metres.
Hence the required length of the train = 100 metres.

(Note you may say that this is so long but dear this is the only way to explain the whole concept of the question to you now its upto you that how fast and short handedly you can solve these type of questions)

Hope you have enjoyed the base concept of this chapter till now. More Conceptual enjoyment with the Various Questions related to this chapter which are frequently asked in the examinations will be presented to your for self study on this blog soon, just keep visiting this blog regularly and writing me your related queries through comment or forum.

More types of questions will be followed soon on this blog........................


Best of Luck for your upcoming Exams. To be continued soon........................

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