Problems on Trains - Concept 2, Quantitative Aptitude Video Lecture | Quantitative Aptitude (Quant) - CAT

welcome to train for aptitude in today's
session we discuss about the second
concept in the problems related to train
let us now look at the problem a train
moving at 85 km/h overtakes a man
running in the same direction as the
train at 13 km/h in 9 seconds what is
the length of the train our options are
a 810 meters be 225 meters C 180 meters
be 648 meters let us now begin
visualizing the problem the train is
moving at 85 kilometers per hour in the
direction as shown the person is also
moving at 13 kilometers per hour in the
same direction an important underlying
assumption in these kinds of problems is
that the train and man both move at a
steady pace throughout the distance also
note that the width of the person is
extremely negligible compared to the
length of the train and therefore we can
neglect that additional distance the
second important thing to note is the
units of measuring the units of
measuring the speed of the train and the
person are in kilometers per hour while
the time to overtake is given in seconds
we would need to make these units
uniform let us now look at the second
visualization in this scenario the train
has overtaken the individual running
what is important to note here is that
while the train was overtaking the
individual continued running at a
constant pace however the total distance
that the train would have covered in
order to completely overtake him would
be the length of the Train and the
dimension of the person however given
that the dimension of the person is
extremely small we can neglect that and
therefore the distance covered by the
training is nothing but the length of
the train itself
at this juncture we would also need to
make a choice and how we would go about
solving the problem one way is to
calculate the total distance that the
train would have covered in that time
then subtract the total distance
travelled by the person at that speed
within the duration of nine seconds the
second approach is that we look at only
the relative speed of the two objects
that is the train and the individual and
calculate the actual distance traveled
using relative speed approach we would
prefer doing it the second way let us
now solve the problem what is given to
us is that the speed of the train is 85
kilometres per hour the speed of the
person is 13 kilometers per hour and
both these are moving in the same
direction the time taken to overtake the
person is nine seconds step one is
calculation of the relative speed the
direction of the person and the train
are the same so we would need to
subtract the speed of the person from
the speed of a train to calculate the
relative speed in this case it is 72
kilometers per hour the next step is
that we need to get the units of
calculation consistent with that of the
time we do that as in the earlier
example and we have the speed of a train
as 20 meters per second the next step is
pretty simple you will need to calculate
the distance covered by the train in
that time which is 20 meters per second
into 9 or 180 meters that is the answer
let us now try to generalize it we begin
with first looking at what is given to
us the speed of the train the speed of
the person and the time taken to
overtake the next step to generalization
is that of calculating the relative
speed
depending on whether the person is going
in the same direction or in the opposite
direction you will need to take a choice
on the signs of relative speed you would
need to note that in this case we have
already calculated the relative speeds
unlike in the earlier concept where we
first made the unit's uniform and then
made the relative speed calculation this
is simply to avoid the additional
calculations that were made one would
need to do we have already calculated
the speeds in the relative terms the
time taken and now it is just a matter
of calculating the distance using the
standard formula that a speed into time
and therefore we reach the answer thank
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