Question

A train travelling at $36$ km/hr passes in $12$ seconds another train half its length travelling in the opposite direction at $54$ km/hr, If it also passes a railway platform in $1\frac{1}{2}$ minutes what is the length of the platform?

• A. $800$ m
• B. $700$ m
• C. $900$ m
• D. $1000$ m

Answer 1

Answer: (B)

$700$ m

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

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

Relative speed $=(36+54)$ km/hr $=90$ km/hr
$=(90\times \frac{5}{18})$ m/s $=25$ m/s

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

$\Rightarrow \frac{3x}{2}=300$

$\Rightarrow x=200$
$\therefore$ Length of the first train $=200$ m

Let the length of the platform be $y$ metres

Speed of the first train $=$ $(36\times \frac{5}{18})$ m/s $=10$ m/s
$\therefore (200+y)\times \frac{1}{10}=90$

$\Rightarrow 200+y=900$

$\Rightarrow y=700$ m