Question

A train passes a platform $90$ m long in $30$ seconds and a man standing on the platform in $15$ seconds. The speed of the train is:

• A. $12.4$ km/hr
• B. $14.6$ km/hr
• C. $18.4$ km/hr
• D. $21.6$ km/hr

Answer 1

The correct option is D $21.6$ km/hr

Let the speed of the train be x m/sec and length of the train be y m. Then,

$\frac{\text{Length of the train}}{\text{Speed of the train}}=$ Time taken by the train to pass the man

$\Rightarrow \frac{y}{x}=15\Rightarrow y=15x$ ......... (1)

and $\frac{\text{Length of train + Length of platform}}{Speedoftrain}=$ Time taken by the train to cross the platform

$\Rightarrow \frac{y+90}{x}=30\Rightarrow y+90=30x$ ........ (2)

Put the value of y from (1) in (2)

$15x+90=30x\Rightarrow 15x=90\Rightarrow x=6m/sec$

$\therefore$ Speed of train $=(6\times \frac{18}{5})km/hr=21.6km/hr$.