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 in passing 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

The correct option is A $25.2$ km/hr

Let the length of the train be $x$ metres

Then Speed of he train in passing through he platform $\frac{x+84}{21}$ m/sec
and speed of the train in passing the man $=$ $\frac{x}{9}$ m/sec.
Since both the speeds are the same,
$\frac{x+84}{21}=\frac{x}{9}$

$\Rightarrow 9x+756=21x$

$\Rightarrow 12x=756$

$\Rightarrow x=\frac{756}{12}=63$ m
$\therefore$ speed of the train $=$ $\frac{(63+84)}{21}$ m/sec $=7$ m/sec $=$ $7\times \frac{18}{5}$ km/hr $=25.2$ km/hr