Question

A train is travelling at 48 kmph completely crosses another train having half its length and travelling in the opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is
A. 400 m
B. 450 m
C. 560 m
D. 600 m

Answer 1

Hint: This is a simple problem of time and distance. First of all we have to know basic concepts of time, distance and speed .Distance means a gap between two fixed destinations or points which can be measured in any unit of length like cm,m km,etc. Then , time is total duration which can be measured in seconds, minutes, hours,etc.Speed is the ratio of total distance travelled to the total time taken to reach from an initial point to final point or destination.
So, this is related to solving systems of equations and trying to get a common solution to the equation. In certain problems where we deal with unknown/s for finding their solution which comes under the Linear equation.

Complete step-by-step answer:
GIVEN: The train is travelling with 48 kmph and another train of half of its length with 42 kmph speed.
Hence, if the length of former train is x metres then it will have relative speed of (48+42)kmph
= 90 kmph=90×$\dfrac{5}{{18}}$ =25 metres per second(mps) and it takes 12 seconds.
(if two objects move in opposite direction then their relative speed is the sum of their individual speeds and they move in same direction then their relative speed is the difference of their individual speeds)
As, distance = speed× time
So,x+$\dfrac{x}{2}$ =25×12
Then,x= 200 m
Let the length of platform be ‘l’ metres
And now the train takes 45 seconds to cross the platform.
Then again, distance = speed× time
So, l+200 = speed of train × 45
Then, l+200 = 48×$\dfrac{5}{{18}}$ × 45 …………..(48 kmph=48×$\dfrac{5}{{18}}$ mps)
Then, l+200 =600
Hence, l =400 m (OPTION A IS CORRECT)

Note: Proper conversion should be made i.e. from minutes to hours or vice-versa while solving problems. And if speed is in kmph then time should be in hours and distance should be in km.