Question

A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is

• A. $400m$
• B. $200m$
• C. $600m$
• D. $250m$

Answer 1

The correct option is A $400m$

Let the length of the first train be $x$ metres

length of the second train$=\frac{x}{2}$m

relative speed of the two trains$=48+42$

$=90kmph$

$=90\times \frac{5}{18}$

$=25m/s$

$25=\frac{x+\frac{x}{2}}{12}$

$25=\frac{2x+x}{24}$

$3x=25\times 24$

$x=25\times 8$

$x=200$

So, the length of the train $=200m$

Let the length of the platform be y

Speed of the train $=48kmph$

$=48\times \frac{5}{18}$

$=\frac{40}{3}m/s$

$\frac{40}{3}=\frac{200+y}{45}$

$40\times 45=600+3y$

$1800=600+3y$

$3y=1200$

$y=400$

So, the length of the platform$=400m$