Question : A train passes two bridges of lengths 400 metres and 200 metres in 80 seconds and 60 seconds, respectively. What is the length (in metres) of the train?
Option 1: 200
Option 2: 400
Option 3: 350
Option 4: 720
Correct Answer: 400
Solution :
Let the speed of the train be $y$ m/s and the length of the train be $x$ metres.
$\text{Speed}=\frac{\text{Distance}}{{\text{Time}}}$
Case – 1:
Total distance = ($x+400$) m
Time = 80 seconds
$y=\frac{x+400}{80}$ ---(1)
Case – 2:
Total distance = ($x+200$) m
Time = 60 seconds
$y=\frac{x+200}{60}$ ---(2)
From equation (1) and (2), we get,
$\frac{x+400}{80}=\frac{x+200}{60}$
⇒ $3x+1200=4x+800$
$\therefore x = 400$
Hence, the correct answer is 400 metres.
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