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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