Question

A person standing on a railway platform noticed that a train took 21 seconds to completely pass through the platform which was 84 m long and it took 9 seconds to pass him. What was the speed of the train?
A) 25.2 km/hr
B) 32.4 km/hr
C) 50.4 km/hr
D) 75.6 km/hr

Answer 1

Hint: In this question it is given that a person standing on a railway platform noticed that a train took 21 seconds to completely pass through the platform which was 84 m long and it took 9 seconds to pass him. We have to find the speed of the train. So to find the solution we first need to find the length of the train and after that we can easily find the speed of the train. So for this
We have to know the formula of speed,
 i,e, $$speed=\dfrac{distance}{time}$$.........................(1)
Complete step-by-step solution:
Let the length of the train be x meters.
As it is given in the question that the length of the platform is 84 m. So if the train passes the platform in 21 seconds, then the distance covered by the train = (x+84) m.
Now by equation (1) we can write the speed of the train,
S=$$\dfrac{\left( x+84\right) }{21}$$ m/sec. ………………(2)
Now another information is that the train passes the person in 9 seconds, and as we know that when a train passes a person or a pole then distance covered by the train will be its length, i.e, distance =x meters.
So by equation (1) we can write, the speed of the train,
S=$\dfrac{x}{9}$ m/sec. ……………………..(3)
Now, from equation (2) and (3) we can write,
$$\dfrac{\left( x+84\right) }{21}$$=$$\dfrac{x}{9}$$
$\Rightarrow \left( x+84\right) \times 9=21x$
$\Rightarrow 9x+756=21x$
$\Rightarrow 21x=9x+756$
$\Rightarrow 21x-9x=756$
$\Rightarrow 12x=756$
$$\Rightarrow x=\dfrac{756}{12}$$
$\Rightarrow x=63$
So the length of the train is 63 m.
Therefore, from equation (3) we can find the speed of the train,
S=$$\dfrac{x}{9}$$ m/sec
  =$$\dfrac{63}{9}$$ m/sec
since as we know that 1 m=$$\dfrac{1}{1000}$$ km and 1 sec =$$\dfrac{1}{3600}$$ hr, so by this above value can be written as,
S=$$\dfrac{63}{9} \times \dfrac{3600}{1000}$$ km/hr
  =$$\dfrac{7\times 36}{10}$$ km/hr
  =$$\dfrac{252}{10}$$ km/hr
  =25.2 km/hr
So we can say the speed of the train is 25.2 km/hr.
Hence the correct option is option A.
Note: To solve this type of question you need to know that when a train passes a railway platform then the train needs to cover the distance of platform as well as the distance of its own length and when the train passes a pole or a person then the train needs to cover only the distance which is equal to its length.