Question

25. A 280 metres long train, travelling at a uniform
speed, crosses a platform in 60 seconds and a
man standing on the platform in 20 seconds.
What is the length of the platform ?
(1) 640 metres
(2) 560 metres
(3) 280 metres
(4) Cannot be determined​

Answer 1

Given :-  

• Length of train is 280 m  
• Crosses a platform in 60 sec  
• Crosses a man standing on platform in 20 sec  
• It is moving at uniform speed  

To Find :-  

• Length of the platform  

Solution :-  

~Here , we’re given the length of train and time taken by it to cross a platform and a man . As the speed is uniform , it’s speed will be same to cover both the distances and we’re given the time taken . From here we can easily find the distance of the platform by putting the values in the formula of finding the speed.

 

Let the length of the platform be ‘ x ‘  

Speed of train while crossing the man and platform is same and we know that ,  

$\sf Speed = \dfrac{Distance}{Time}$

While crossing the platform ::  

$\sf speed = \dfrac{280+x}{60}$

While crossing the man ::  

$\sf speed = \dfrac{280}{20}$

As the speed is equal , the equation formed will be  

$\sf \implies \dfrac{280+x}{60} = \dfrac{280}{20}$  

$\sf \implies \dfrac{280+x}{60} = 14$

$\sf \implies 280 + x = 14( 60 )$

$\sf \implies 280 + x = 840$

$\sf \implies x = 840- 280$  

$\sf \implies x = 560$

Therefore ,  

Length of the platform is 560 m  

Answer 2

⠀⠀⠀⠀⠀⠀⠀${\rm{\purple{\underline{\underline{★Required \:Answer★}}}}}$

560 metres

⠀⠀⠀⠀⠀${\rm{\pink{\underline{\underline{★Solution★}}}}}$

${\rm{\red{\underline{\underline{Given : }}}}}$

• A train of length 280 m.
• It crosses a platform and man in 60 secs and 20 secs respectively.

${\rm{\blue{\underline{\underline{To \: Find: }}}}}$

• Length of the platform.

${\rm{\purple{\underline{\underline{Formula \: Used: }}}}}$

$\rm \: v = \frac{d}{t}$

where,

v = speed of the train

d = distance covered by train

t = time taken by the train to cover the distance in secs.

${\rm{\orange{\underline{\underline{Calculations : }}}}}$

Let the length of the platform be 'L'

When the train crosses the man completely,

The distance covered by it = 280 m

Time Taken = 20 secs

Therefore,

Speed of the train :-

$\longrightarrow\rm \: v = \frac{d}{t}$

$\longrightarrow\rm \: v = \frac{280}{20}$

$\longrightarrow\rm\red{ \: v = 14 \:metre/second}$

Now, let's find out the length of the platform :-

When it crosses the platform distance covered by it :- 280 + L

Time taken to cross the platform = 60 secs

Speed of the train = 14 m/s

Therefore,

Distance = Time × Speed

substituting the values,

↝280 + L = 60 × 14

↝280 + L = 840

↝L = 840 - 240

↝L = 560 metres

Hence, the length of the platform is 560 metres.