Problem on
Trains is an another important topic of chapter Time Speed and Distance from
competition point of view. In the previous posts 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:-
·
Suppose two trains are
moving in the opposite directions at speed x m/sec. and y m/sec., then their
relative speed = (x + y) m/sec.
· If two trains of length
l1 metres and l2 metres are moving in opposite directions
at x m/sec. and y m/sec.,
then time taken by the trains to cross each other = [(l1
+ l2)/(x + y)] sec.
·
Suppose two trains are
moving in the same directions at speed x m/sec. and y m/sec., then their
relative speed = (x ─ y) m/sec.
·
If two trains of length
l1 metres and l2 metres are moving in same directions at
x m/sec. and y m/sec.,
then time taken by the trains to cross each other = [(l1
+ l2)/(x ─ y)] sec.
Q7. Two trains 90m and 60m long respectively, run at the rates of
90km and 54kms. an hour on parallel rails in same directions. How long do they
take to pass each other?
Note :- In this type of questions the only thing to be noticed is
that all the dimensions should be same unit scale means either distance in kilometres and time in hours or
distance in metres and time in seconds. These questions are based on relative
speed concept.
As we have discussed in the previous post of this topic that in
such questions:-
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
Sol. Analyse the given data
in the question:
l1 = 90m, l2
= 60m, Speed of 1st train
(x) = 90 kms./hr.
Speed of 2nd train (y) = 54 kms./hr.
Distance travelled by the trains to cross each other = 90 + 60 =
150m
Relative speed (Trains moving in same direction) = 90 ─ 54 = 36
kms./hr.
= 36 ×
(5/18) = 10 m/sec.
Formula used in such questions:
Time taken = Total distance/(Relative speed)
Putting the values;
Time taken = 150/10 = 15
secs.
Hence the
required time taken by trains to cross each other is 15secs.
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Q8. A train, 130 meters long running with a speed of 70 km/hr. How
long does it take to cross another train 150 meters long travelling at 56
km/hr in the opposite direction?
Sol. Analyse the given
data in the question:
l1 = 130m,
l2 = 150m, Speed
of 1st train (x) = 70 kms./hr.
Speed of 2nd train (y) = 56 kms./hr.
Distance travelled by the trains to cross each other = 130 + 150
= 280m
Relative speed (Trains moving in opposite direction) = 70 + 56 =
126 kms./hr.
= 126 × (5/18) = 35 m/sec.
Formula used in such questions:
Time taken = Total distance/(Relative speed)
Putting the values;
Time taken = 280/35 = 8
secs.
Hence
the required time taken by trains to cross each other is 8secs.
Q9. Two trains are travelling in the opposite direction at
40km/hr. and 32 km/hr. The faster
train crosses a man sitting in the slower train in just 6 secs. Find
the length of the faster train.
Note: In such question faster trains crosses a man sitting in
the slower train indicates that the faster train is crossing a stationary man
or you can say a pole. In such questions only the length of the faster train
can be determined as the distance travelled in such questions is equal to the
length of the faster train. In this
type of questions the length of the length of the slower train can never be
determined.
Sol. Analyse the given
data in the question:
Speed of 1st train (x) = 40 kms./hr.
Speed of 2nd
train (y) = 32 kms./hr.
Time taken to cross the man sitting in the slower train = 6
secs.
Distance travelled by the trains to the man sitting in slower
train = length of faster train
Relative speed (Trains moving in opposite direction) = 40 + 32 =
72 kms./hr.
= 72 × (5/18) = 20 m/sec.
Formula used in such questions:
Time taken = Total distance/(Relative speed)
Putting the values;
6 = Total distance/20
→ Total distance =
length of the faster train = 6 × 20
length of the faster train
= 120meters
Hence
the required length of the faster
train is 120meters only.
(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 CGL Exams. To be continued soon........................
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