GATE Mechanical Engineering (ME) 2018 Shift 1 Solved Paper

Question : 10 of 65

Marks: +1, -0

From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while travelling at a constant speed of

54 {km} {/} {h}

. At the same speed, it takes 14 seconds to pass a man running at

9 {km} {/}{h}

in the same direction as the train. What is the length of the train and that of the platform in meter, respectively?

$210$ and $140$
$162.5$ and $187.5$
$245$ and $130$
$175$ and $200$

Validate

Solution:

Train speed

= 54

km/h
Time

= 25

sec for travelling length of train and length of platform
Man speed

= 9

km/h
Relative speed of train with respect to man

= 45

km/h
Time

= 14

sec
So, length of train = time × speed

=14 × 45 × \;{5}/{18}

Length of train

=35 × 5 {m}=175 {m}

Length of platform

+

length of train

=

speed

\times

time

=54 × \;{5}/{18} × 25=15 × 25=375 {m}

Length of platform

=375-175=200 {m}

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