Question

A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
$
  (a){\text{ 120 metres}} \\
  (b){\text{ 180 metres}} \\
  (c){\text{ 324 metres}} \\
  (d){\text{ 150 metres}} \\
$

Answer 1

- Hint – In this question the distance travelled by the train at the given speed and the time will be the actual length of the train, so use the direct basic relation between distance, speed and time that is distance is the product of speed and time, to get the answer.

Complete step-by-step solution -

Given data:
Speed (v) of train = 60 km/hr.
And it takes 9 seconds to cross a pole.
Therefore time (t) = 9 seconds.
Now as we know 1 km = 1000 meter.
And 1 hr. = 3600 sec.
So 1(km/hr.) = (1000/3600) = (5/18) meter/seconds
So 60 km/hr. = $60 \times \dfrac{5}{{18}} = \dfrac{{50}}{3}$ m/sec.
So the speed (v) of the train = $\dfrac{{50}}{3}$ m/sec.
Now as we know speed (v), distance (s) and time (t) is related as
$s = v \times t$ Units.
Now let the length of the train be l m.
$ \Rightarrow l = v \times t$ Meters.
Now substitute the values in above equation we have,
$ \Rightarrow l = \dfrac{{50}}{3} \times 9 = 150$ Meters.
So this is the required answer.
Hence option (D) is correct.

Note – In this question the options that is the length of the train is asked in meters and the speed is given in km/hr although the time was given in sec, so as to synchronize the units in order to get the answers in meters the conversion of km/hr is done into m/sec. Here we have assumed that initially the train’s main engine was at the starting of the pole so when it entirely crosses the pole all its boogies must have crossed the pole that’s why the distance traveled is taken as the length.